Cham: Springer, 2025. — 550 p. Preface Local Colligations and Model Representations of Linear Non-Self-Adjoint Bounded Operators Local Colligations. Open Systems. Characteristic Functions Dilations of Semigroups. The Scattering Operator Translational and Functional Models Diagonal of an Open System. Existence Theorem Triangular Models Universal and Functional Models of...
Basel: Birkhäuser, 2011. — 283 p. New methods for solving classical problems in the theory of nonlinear operator equations (solvability, multiple solutions, bifurcations, nonlinear resonance, potential methods, etc) are introduced and discussed. The general abstract theorems are illustrated by various applications to differential equations and boundary value problems. In...
Springer Nature Switzerland, 2024. — 145 p. Supervisor’s Foreword Abstract Publications Related to This Thesis Acknowledgements Acronyms Introduction Operator Growth in Krylov Space Dispersion Bound on Krylov Complexity A Brief History of Quantum Speed Limits in Isolated Systems QSLs on Operator Flows QSLs on Correlation Functions A Geometric Operator Quantum Speed Limit...
М.: МГУ, 2024. — 173 с. Целью учебного пособия является изложение теории обобщенных функций, ее методов и применения к решению задач математической физики в различных пространствах. В книге рассматриваются основные пространства обобщенных функций, в том числе пространства обобщенных функций медленного роста и пространства Соболева. Большое внимание уделяется методам, связанным...
Springer, 2024. — 341 p. This book is a comprehensive and advanced exploration of trace inequalities in the context of matrices and operators acting on Hilbert spaces. Its goal is to present elegant inequalities with innovative proofs. Instead of presenting generalized versions that can be complicated and lack clarity, the book focuses on beautiful and original inequalities....
Basel: Birkhäuser, 2024. — 352 p. The purpose of the present book is to develop the counterparts of Banach and Hilbert spaces in the setting of slice hyperholomorphic functions. Banach and Hilbert spaces of analytic functions, in one or several complex variables, play an important role in analysis and related fields. Besides their intrinsic interest, such spaces have numerous...
Basel: Birkhäuser, 2024. — 519 p. The present monograph serves as a natural extension of the prior 2-volume monograph with the same title and by the same authors, which encompassed findings up until 2014. This four-volume project encapsulates the authors’ decade-long research in the trending topic of nonstandard function spaces and operator theory. One of the main novelties of...
Berlin: de Gruyter, 2023. — 460 p. — (De Gruyter Studies in Mathematics 94). This is the first treatment entirely dedicated to an analytic study of spectral flow for paths of selfadjoint Fredholm operators, possibly unbounded or understood in a semifinite sense. The importance of spectral flow for homotopy and index theory is discussed in detail. Applications concern...
Springer, 2024. — 354 p. The book contains a collection of more than 800 problems from all main chapters of functional analysis, with theoretical background and solutions. It is mostly intended for undergraduate students who are starting to study the course of functional analysis. The book will also be useful for graduate and post- graduate students and researchers who wish to...
North Holland, 1988. — 373 p. This monograph only requires of the reader a basic knowledge of classical analysis: measure theory, analytic functions, Hilbert spaces, functional analysis. The book is self-contained, except for a few technical tools, for which precise references are given.Part I starts with finite-dimensional spaces and general spectral theory. But very soon...
Hoboken: Wiley, 1989. — 315 p. A monograph on the fundamentals of the theory of linear operators in spaces with an indefinite metric. Introduces the geometry of spaces with indefinite metric, and the central topics of operator theory, and explores variations on the theme. The theory is set out in Krein and Pontryagin spaces, with passing reference made to generalizations to...
Basel: Birkhäuser, 2024. — 502 p. This monograph proposes a unified theory of the calculus of fractional and standard derivatives by means of an abstract operator-theoretic approach. By highlighting the axiomatic properties shared by standard derivatives, Riemann-Liouville and Caputo derivatives, the author introduces two new classes of objects. The first class concerns...
М.: ВИНИТИ, 1989. — 250 с. Статья представляет собой обзор современной спектральной теория дифференциальных операторов в частных производных. Обсуждаются вопросы о самосопряженности таких операторов, о характере их спектра. Описаны различные методы получения спектральных асимптотик и имеющиеся формулы асимптотик спектральной функции и собственных значений. Изложены методы...
New York : Springer-Verlag, 1980. — xiii, 402 p. — (Graduate texts in mathematics). This English edition is almost identical to the German original Lineare Operatoren in Hilbertriiumen, published by B. G. Teubner, Stuttgart in 1976. A few proofs have been simplified, some additional exercises have been included, and a small number of new results has been added (e.g., Theorem...
Springer, 2024. — 222 p. This book explains the basic theory of Hilbert C*-module in detail, covering a wide range of applications from generalized index to module framework. At the center of the book, the Beurling-Deny criterion is characterized between operator valued Dirichlet forms and quantum Markov semigroups, hence opening a new field of quantum probability research. The...
Springer, 2024. — 277 p. The main goal of this book is to describe various aspects of the theory of joint spectra for matrices and linear operators. It is suitable for a graduate-level topic course in spectral theory and/or representation theory. The first three chapters can also be adopted for an advanced course in linear algebra. Centered around the concept of projective...
Basel: Birkhäuser, 2007. — 242 p. This volume contains contributions written by participants of the 4th Workshop on Operator Theory in Krein Spaces and Applications, held at the TU Berlin, Germany, December 17 to 19, 2004. The workshop covered topics from spectral, perturbation, and extension theory of linear operators and relations in inner product spaces.
Springer, 2021. — 194 p. This unique book contains a generalization of the Leray-Schauder degree theory which applies for wide and meaningful types of discontinuous operators. The discontinuous degree theory introduced in the first section is subsequently used to prove new, applicable, discontinuous versions of many classical fixed-point theorems such as Schauder’s. Finally,...
М.: Наука, 1986. — 352 с. В книге на базе геометрии пространств с индефинитной метрикой — главным образом пространств Крейна и Понтрягина — развиты основы теории линейных операторов в этих пространствах, включая теорию инвариантных подпространств, спектральные вопросы и вопросы расширения операторов. Приведены также некоторые приложения. Книга рассчитана на математиков —...
Москва: Государственное издательство физико-математической литературы, 1962. — 323 с. Общая теория операторов обобщенного сдвига Прямые теоремы Ли для операторов обобщенного сдвига Обратные теоремы Ли для операторов обобщенного сдвига в одномерном действительном случае Некоторые применения операторов обобщенного сдвига в одномерном действительном случае Решение обратной задачи...
Cambridge: Cambridge University Press, 1990. — 317 p. Aiming to present a self-contained account of the present state of knowledge of the theory of the non-linear superposition operators - a generalization of the notion of functions - this book diverges from classical nonlinear analysis and is applicable to operators in a variety of function spaces.
Springer, 1996. — 255 p. The theory of vector lattices, stemming from the mid-thirties, is now at the stage where its main achievements are being summarized. The sweeping changes of the last two decades have changed its image completely. The range of its application was expanded and enriched so as to embrace diverse branches of the theory of functions, geometry of Banach...
Essex: Longman Scientific & Technical; Wiley, 1987. — 146 p. The author has written this introduction to semigroups of linear operators for anyone with an Honours student's knowledge of complex and functional analysis preferably, though not essentially, including the Lebesgue integral. His first chapter explains the notion of a one-parameter semigroup, and discusses four...
Basel: Birkhauser, 2023. — 583 p. Preface Acknowledgments A Review of Relevant Operator Theory Bounded Hilbert Space Operators Topologies on the Space B( H) The Lattice of Projections Closed Linear Operators The Spectral Theorem Self-adjoint operators Polar Decomposition Quadratic Forms Algebras with an Involution C-Algebras Von Neumann Algebras Singular Functionals on von...
Springer, 2023. — 364 p. This book provides a comprehensive analysis of the existence of weak solutions of unsteady problems with variable exponents. The central motivation is the weak solvability of the unsteady p(...)-Navier–Stokes equations describing the motion of an incompressible electro-rheological fluid. Due to the variable dependence of the power-law index p(...) in...
Berlin: de Gruyter, 2023. — 266 p. This book presents a wide-ranging approach to operator-valued measures and integrals of both vector-valued and set-valued functions. It covers convergence theorems and an integral representation for linear operators on spaces of continuous vector-valued functions on a locally compact space. These are used to extend Choquet theory, which was...
Berlin: Springer-Verlag, 2009. — 369 p. Integration theory deals with extended real-valued, vector-valued, or operator-valued measures and functions. Different approaches are applied in each of these cases using different techniques. The order structure of the (extended) real number system is used for real-valued functions and measures, whereas suprema and infima are replaced...
Cham: Springer Nature Switzerland, 2023. — 263 p. This text covers a first course in bilinear maps and tensor products intending to bring the reader from the beginning of functional analysis to the frontiers of exploration with tensor products. Tensor products, particularly in infinite-dimensional normed spaces, are heavily based on bilinear maps. The author brings these topics...
НИЦ Инфра-М, 2020. — 296 с. Монография посвящена приложению методов функционального анализа к вопросам качественной теории дифференциальных уравнений. Изложен алгоритм приведения дифференциальной краевой задачи к операторному уравнению. Выполнено исследование решений операторных уравнений специального вида в пространствах, полуупорядоченных при помощи конуса, где ограниченность...
De Gruyter, 2023. — 336 p. This book's subject lies in the nexus of partial differential equations, operator theory, and complex analysis. The spectral analysis of the complex Laplacian and the compactness of the d-bar-Neumann operator are the primary topics of the section. The revised 2nd edition explores the Segal Bargmann Space (Fock space) connection to quantum mechanics,...
Казань: Казанский государственный университет (КГУ), 2007. — 99 с. Линейное пространство Линейное пространство Линейная зависимость и ее свойства Базис и размерность Координаты. Изоморфизм пространств Координаты вектора в новом базисе Сумма и пересечение пространств Прямые суммы Линейные операторы Линейные отображения векторных пространств Матрица линейного оператора Алгебра...
Mdpi AG, 2019. — 210 p. A plethora of problems from diverse disciplines such as Mathematics, Mathematical: Biology, Chemistry, Economics, Physics, Scientific Computing and also Engineering can be formulated as an equation defined in abstract spaces using Mathematical Modelling. The solutions of these equations can be found in closed form only in special case. That is why...
Springer, 2004. — 404 p. This is the first monograph devoted to a fairly wide class of operators, namely band and band-dominated operators and their Fredholm theory. The main tool in studying this topic is limit operators. Applications are presented to several important classes of such operators: convolution type operators and pseudo-differential operators on bad domains and...
De Gruyter, 2020. — 288 p. The central question in this monograph is to what extent the Hermitian part of a linear operator determines its properties. Various properties are investigated and some applications of the theory are given. Chapter 1 deals with some results from operator theory and the theory of extensions. Chapter 2 is devoted to the investigation of regular...
De Gruyter, 2023. — 498 p. Continuous model theory is an extension of classical first order logic which is best suited for classes of structures which are endowed with a metric. Applications have grown considerably in the past decade. This book is dedicated to showing how the techniques of continuous model theory are used to study C*-algebras and von Neumann algebras. This book...
Cham: Birkhäuse, 2022. — 605 p. This monograph provides a state-of-the-art, self-contained account on the effectiveness of the method of boundary layer potentials in the study of elliptic boundary value problems with boundary data in a multitude of function spaces. Many significant new results are explored in detail, with complete proofs, emphasizing and elaborating on the link...
Princeton University Press, 2011. — 343 p. This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow. It is essentially the weighted sum of a harmonic...
Princeton University Press, 2008. — 378 p. This book presents the analytic foundations to the theory of the hypoelliptic Laplacian. The hypoelliptic Laplacian, a second-order operator acting on the cotangent bundle of a compact manifold, is supposed to interpolate between the classical Laplacian and the geodesic flow. Jean-Michel Bismut and Gilles Lebeau establish the basic...
ITexLi, 2023. — 167 p. — ISBN 1838811117, 9781838811112, 1838809929, 9781838809928, 1838811125, 9781838811129. Operator theory is a fascinating model that includes essential theorems and diverse applications in all science. This book discusses some fundamental aspects of pure and applied operator theory and the use of the theory to solve a large array of problems. As such, it...
Springer. — 2012. — 434 p. — (Graduate Texts in Mathematics 265). — ISBN 978-94-007-4752-4. Неограниченные самосопряженные операторы в гильбертовом пространстве The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger operators) and analysis...
Berlin: Springer, 1970. — 458 p. Preface Table of Contents Introduction Exponential representation for an ordinary equation with one unknown function Exponential representation of the solutions of partial differential equations The exponential representation of solutions of arbitrary systems Analytic Methods Homological Tools Families of topological modules The fundamental...
Berlin: Springer, 2008. — 127 p. This volume introduces an entirely new pseudodifferential analysis on the line, the opposition of which to the usual (Weyl-type) analysis can be said to reflect that, in representation theory, between the representations from the discrete and from the (full, non-unitary) series, or that between modular forms of the holomorphic and substitute for...
Basel: Birkhäuser, 2003. — 249 p. Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2002. The subject of this book is the study of automorphic distributions, by which is meant distributions on R2 invariant under the linear action of SL(2,Z), and of the operators associated with such distributions under the Weyl rule of symbolic calculus. Researchers and...
Basel: Birkhauser, 2008. — 150 p. Consists entirely of new material Contents is related to the book Automorphic pseudodifferential analysis and higher-level Weyl calculi (appeared in Progress in Mathematics) by the same author: one-dimensional pseudo-differential analysis is considered in both volumes; however, the results are disjoint: the former book dealt with automorphic...
Berlin: Springer, 2000. — 260 p. This is a new approach to the theory of non-holomorphic modular forms, based on ideas from quantization theory or pseudodifferential analysis. Extending the Rankin-Selberg method so as to apply it to the calculation of the Roelcke-Selberg decomposition of the product of two Eisenstein series, one lets Maass cusp-forms appear as residues of...
ITexLi, 2023. — 96 p. — ISBN 1803563338 9781803563336 180356332X 9781803563329 1803563346 9781803563343. This book covers recent developments in the field of functional calculus. Calculus is the elementary subject of applied analysis and its study provides a rich variety of functions and their behavior. The book brings together a range of different but related concepts from...
Oxford: Oxford University Press, 2023. — 529 p. Aimed at graduate students, this textbook provides an accessible and comprehensive introduction to operator theory. Rather than discuss the subject in the abstract, this textbook covers the subject through twenty examples of a wide variety of operators, discussing the norm, spectrum, commutant, invariant subspaces, and interesting...
Amsterdam: Springer, 1994. — 303 p. This book is devoted to the Fredholm theory of singular integral operators with shift in Lp, 1 Front Matter Background Information Noetherity criterion and a formula for the index of a singular integral functional operator of first order in the continuous case The Noether theory of a singular integral functional operator of finite order in...
Basel: Birkhäuser, 2015. — 490 p. This proceedings volume originates from a conference held in Herrnhut in June 2013. It provides unique insights into the power of abstract methods and techniques in dealing successfully with numerous applications stemming from classical analysis and mathematical physics. The book features diverse topics in the area of operator semigroups,...
Cham: Springer, 2023. — 225 p. This book contains a self-consistent treatment of Besov spaces for W*-dynamical systems, based on the Arveson spectrum and Fourier multipliers. Generalizing classical results by Peller, spaces of Besov operators are then characterized by trace class properties of the associated Hankel operators lying in the W*-crossed product algebra. These...
Basel: Birkhäuser, 2015. — 418 p. The theoretical part of this monograph examines the distribution of the spectrum of operator polynomials, focusing on quadratic operator polynomials with discrete spectra. The second part is devoted to applications. Standard spectral problems in Hilbert spaces are of the form A-λI for an operator A, and self-adjoint operators are of particular...
Springer, 2022. — 277 p. This book publishes original research chapters on the theory of approximation by positive linear operators as well as theory of sequence spaces and illustrates their applications. Chapters are original and contributed by active researchers in the field of approximation theory and sequence spaces. Each chapter describes the problem of current importance...
Basel: Birkhäuser, 1989. — 399 p. Linearizations Definitions and examples Uniqueness of linearization Existence of linearizations Operator polynomials that are multiples of identity modulo compacts Inverse linearization of operator polynomials Exercises Notes Representations and Divisors of Monic Operator Polynomials Spectral pairs Representations in terms of spectral pairs...
New York: Springer, 2012. — 123 p. Inequalities of Ostrowski and Trapezoidal Type for Functions of Selfadjoint Operators on Hilbert Spaces presents recent results concerning Ostrowski and Trapezoidal type inequalities for continuous functions of bounded Selfadjoint operators on complex Hilbert spaces. The first chapter recalls some fundamental facts concerning bounded...
New York: Springer, 2012. — 134 p. The main aim of this bookis to present recent results concerning inequalities of the Jensen, Čebyšev and Grüss type for continuous functions of bounded selfadjoint operators on complex Hilbert spaces. In the introductory chapter, the author portrays fundamental facts concerning bounded selfadjoint operators on complex Hilbert spaces. The...
Cham: Springer, 2022. — 164 p. This book is essentially a survey of results on the Fuglede-Putnam theorem and its generalizations in a wide variety of directions. Presenting a broad overview of the results obtained in the field since the early 1950s, this is the first monograph to be dedicated to this powerful tool and its variants. Starting from historical notes and classical...
Berlin: Springer, 2002. — 537 p. The method of difference potentials (MDP) was proposed in [1]-[8] and sig nificantly developed in [9]-[101] and some other works. The present book describes the current state of the art in the method of difference potentials and is a revised and essentially supplemented version of the author's first book devoted to this method, which was...
Berlin: de Gruyter, 1997. — 300 p. In this book we are concerned with methods of the variational calculus which are directly related to the theory of partial differential equations of elliptic type. The methods which we discuss and describe here go far beyond elliptic equations. In particular, these methods can be applied to Hamiltonian systems, nonlinear wave equations and...
Boca Raton: CRC Press/Chapman & Hall, 2022. — 229 p. Banach-Space Operators On C*-Probability Spaces Generated by Multi Semicircular Elements introduces new areas in operator theory and operator algebra, in connection with free probability theory.In particular, the book considers projections and partial isometries distorting original free-distributional data on the...
Учебное пособие. — Киев: Наукова думка, 1985. — 145 с. В учебном пособии рассмотрены вопросы теории представлений топологических групп и полугрупп в банаховых пространствах, тесно связанные со спектральной теорией операторов. Существенное внимание уделено методам гармонического анализа. Даны упражнения для самостоятельной работы. Для студентов, аспирантов и преподавателей...
Учебное пособие. — Киев: Наукова думка, 1985. — 145 с. В учебном пособии рассмотрены вопросы теории представлений топологических групп и полугрупп в банаховых пространствах, тесно связанные со спектральной теорией операторов. Существенное внимание уделено методам гармонического анализа. Даны упражнения для самостоятельной работы. Для студентов, аспирантов и преподавателей...
Berlin: de Gruyter, 2022. — 266 p. The book constructs explicitly the fundamental solution of the sub-Laplacian operator for a family of model domains in Cn+1. This type of domain is a good point-wise model for a Cauchy-Rieman (CR) manifold with diagonalizable Levi form. Qualitative results for such operators have been studied extensively, but exact formulas are difficult to...
Cambridge: Cambridge University Press, 2003. — 489 p. The first part of this book is an introduction with emphasis on examples that illustrate the theory of operator spaces. The second part is devoted to applications to C*-algebras, with a systematic exposition of tensor products of C* algebras. The third part of the book describes applications to non self-adjoint operator...
Springer Reference, 2015. — 1846 p. — ISBN 9783034806664. A one-sentence definition of operator theory could be: The study of (linear) continuous operations between topological vector spaces, these being in general (but not exclusively) Fréchet, Banach, or Hilbert spaces (or their duals). Operator theory is thus a very wide field, with numerous facets, both applied and...
Cham: Birkhäuser, 2022. — 358 p. This monograph presents necessary and sufficient conditions for completeness of the linear span of eigenvectors and generalized eigenvectors of operators that admit a characteristic matrix function in a Banach space setting. Classical conditions for completeness based on the theory of entire functions are further developed for this specific...
Cham: Birkhäuser, 2022. — 822 p. Inequalities play a central role in mathematics with various applications in other disciplines. The main goal of this contributed volume is to present several important matrix, operator, and norm inequalities in a systematic and self-contained fashion. Some powerful methods are used to provide significant mathematical inequalities in functional...
Berlin: De Gruyter. 2021. — 416 p. This book is the second edition of the first complete study and monograph dedicated to singular traces. The text offers, due to the contributions of Albrecht Pietsch and Nigel Kalton, a complete theory of traces and their spectral properties on ideals of compact operators on a separable Hilbert space. The second edition has been updated on the...
New York: Springer, 2000. — 451 p. This book presents the main results of the last fifteen years on dominated operators, demonstrating a well-developed theory with a wide range of applications. The exposition focuses on the fundamental properties of dominated operators with special emphasis on their particular classes: integral and pseudointegral operators, disjointness...
Cambridge: Cambridge University Press, 2022. — 511 p. This modern introduction to operator theory on spaces with indefinite inner product discusses the geometry and the spectral theory of linear operators on these spaces, the deep interplay with complex analysis, and applications to interpolation problems. The text covers the key results from the last four decades in a readable...
New York: Springer, 2000. — 632 p. A unique introduction to the theory of linear operators on Hilbert space. The author presents the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians. Although the Definition-Theorem-Proof format of mathematics is used, careful attention is given to motivation of the material covered and...
Basel: Springer, 2010. — 374 p. The book is a commemorative volume honoring the mathematician Paul R. Halmos (1916-2006), who contributed passionately to mathematics in manifold ways, among them by basic research, by unparalleled mathematical exposition, by unselfish service to the mathematical community, and, not least, by the inspiration others found in his dedication to that...
Birkhäuser, 2022. — 612 p. — ISBN 3030978133. This text is the first of its kind exclusively devoted to counterexamples in operator theory and includes over 500 problems on bounded and unbounded linear operators in Hilbert spaces . This volume is geared towards graduate students studying operator theory, and the author has designated the difficulty level for each counterexample...
Basel: Birkhäuser, 2007. — 324 p. This book brings together all available results about the theory of algebraic multiplicities, from the most classic results, like the Jordan Theorem, to the most recent developments, like the uniqueness theorem and the construction of the multiplicity for non-analytic families. Part I (first three chapters) is a classic course on...
Springer, 2021. — 523 p. This book discusses the important aspects of spectral theory, in particular, the completeness of generalised eigenvectors, Riesz bases, semigroup theory, families of analytic operators, and Gribov operator acting in the Bargmann space. Recent mathematical developments of perturbed non-self-adjoint operators are discussed with the completeness of the...
University of Washington, 2017. — 166 p. This dissertation is an amalgamation of various results on the structure of bispectral differential operator algebras, ie. algebras of differential operators with possibly noncommutative coefficients in a variable x satisfying the property of having a family psi(x,y) of joint eigenfunctions which are also eigenfunctions of another...
Basel: Birkhäuser, 2004. — 601 p. Many developments on the cutting edge of research in operator theory and its applications are reflected in this collection of original and review articles. Particular emphasis lies on highlighting the interplay between operator theory and applications from other areas, such as multi-dimensional systems and function theory of several complex...
Cambridge: Cambridge University Press, 2021. — 439 p. This concise monograph explores how core ideas in Hardy space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system theory ideas and reproducing kernel techniques,...
Cambridge: Cambridge University Press, 2021. — 502 p. Starting with elementary operator theory and matrix analysis, this book introduces the basic properties of the numerical range and gradually builds up the whole numerical range theory. Over 400 assorted problems, ranging from routine exercises to published research results, give you the chance to put the theory into practice...
Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, 2001. — 144 p. The main subject of the present monograph is the regularity theory of Fourier integral operators with real and complex phases and related questions of the singularity theory of affine fibrations. It is known that the geometry and singularities of the canonical relation of an operator are...
Монография. — Киев: Наукова думка, 1972. — 220 с. Монография посвящена построению спектральной теории обыкновенных дифференциальных операторов второго порядка с помощью операторов преобразования. Такой подход позволил единым способом и достаточно просто получить все основные результаты спектральной теории как в самосопряженном, так и в несамосопряженном случае. Особое внимание...
Basel: Birkhäuser, 1990. — 616 p. This book aims to present the theory of interpolation for rational matrix functions as a recently matured independent mathematical subject with its own problems, methods and applications. The authors decided to start working on this book during the regional CBMS conference in Lincoln, Nebraska organized by F. Gilfeather and D. Larson. The...
Basel: Birkhäuser, 2000. — 270 p. This book is dedicated to a theory of traces and determinants on embedded algebras of linear operators, where the trace and determinant are extended from finite rank operators by a limit process. All the important classical examples of traces and determinants suggested by Hill, von Koch, Fredholm, Poincar, Ruston and Grothendieck are exhibited....
Basel: Birkhäuser, 2021. — 388 p. The main topics of this volume, dedicated to Lance Littlejohn, are operator and spectral theory, orthogonal polynomials, combinatorics, number theory, and the various interplays of these subjects. Although the event, originally scheduled as the Baylor Analysis Fest, had to be postponed due to the pandemic, scholars from around the globe have...
Cambridge: Cambridge University Press, 2021. — 260 p. Suitable for both postgraduate students and researchers in the field of operator theory, this book is an excellent resource providing the complete proof of the Brown-Douglas-Fillmore theorem. The book starts with a rapid introduction to the standard preparatory material in basic operator theory taught at the first year...
Basel: Birkhäuser, 1996. — 241 p. This book presents a systematic account of the theory of asymptotic behaviour of semigroups of linear operators acting in a Banach space. The focus is on the relationship between asymptotic behaviour of the semigroup and spectral properties of its infinitesimal generator. The most recent developments in the field are included, such as the...
Пер с англ. под ред. Кудрявцева Л.Д. — М.: Наука, 1985. — 160 с. Книга посвящена теории интегральных операторов, которая лежит в основе современного функционального анализа и является богатым источником нетривиальных примеров. Написана лаконично и увлекательно. Основной текст содержит постановки ряда нерешенных проблем. Для научных работников, занимающихся функциональным...
Пер с англ. под ред. Кудрявцева Л.Д. — М.: Наука, 1985. — 160 с. Книга посвящена теории интегральных операторов, которая лежит в основе современного функционального анализа и является богатым источником нетривиальных примеров. Написана лаконично и увлекательно. Основной текст содержит постановки ряда нерешенных проблем. Для научных работников, занимающихся функциональным...
Монография. — Москва: Наука, Главная редакция физико-математической литературы издательства, 1978. — 400 с. Книга посвящена одному из важных направлений функционального анализа - теории интерполяции линейных операторов. Излагаются основные методы построения интерполяционных пространств, изучаются их свойства. Эти методы позволяют с новых позиций взглянуть на ряд тем и...
London: CRC Press, 2001. — 319 p. The book presents a more comprehensive treatment of transmutation operators associated with the Bessel operator, and explores many of their properties. They are fundamental in the complete study of the Bessel harmonic analysis and the Bessel wavelet packets. Many applications of these theories and their generalizations have been injected...
Basel: Birkhäuser, 2021. — 183 p. This textbook introduces some basic tools from the theory of monotone operators together with some of their applications. Examples that work for ordinary differential equations are provided. The illustrating material is kept relatively simple, while at the same time offering inspiring applications to the reader. The material will appeal to...
Springer, 2021. — 413 p. — ISBN 978-3-030-76828-7. This is the second in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University, Rostov-on-Don, Russia. This volume focuses on mathematical methods and...
Springer, 2021. — 413 p. — ISBN 978-3-030-76828-7. This is the second in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University, Rostov-on-Don, Russia. This volume focuses on mathematical methods and...
European Mathematical Society, 2021. — 252 p. — (EMS Series of Lectures in Mathematic). — ISBN 978-3-98547-004-4. The theory of von Neumann algebras, originating with the work of F. J. Murray and J. von Neumann in the late 1930s, has grown into a rich discipline with connections to different branches of mathematics and physics. Following the breakthrough of Tomita–Takesaki...
Springer, 2021. — 523 p. — ISBN 978-981-16-2527-5. This book discusses the important aspects of spectral theory, in particular, the completeness of generalised eigenvectors, Riesz bases, semigroup theory, families of analytic operators, and Gribov operator acting in the Bargmann space. Recent mathematical developments of perturbed non-self-adjoint operators are discussed with...
Springer, 2021. — 523 p. — ISBN 978-981-16-2527-5. This book discusses the important aspects of spectral theory, in particular, the completeness of generalised eigenvectors, Riesz bases, semigroup theory, families of analytic operators, and Gribov operator acting in the Bargmann space. Recent mathematical developments of perturbed non-self-adjoint operators are discussed with...
Apple Academic Press Inc., 2022. — 314 p. — ISBN 978-1-77463-938-2. The concept of multivalued linear operators—or linear relations—is the one of the most exciting and influential fields of research in modern mathematics. Applications of this theory can be found in economic theory, noncooperative games, artificial intelligence, medicine, and more. This new book focuses on the...
AMS. — 298 p. — (Fields Institute Monographs 20). — ISBN 978-0-8218-4800-5. This book provides a comprehensive account of the crucial role automorphic L-functions play in number theory and in the Langlands program, especially the Langlands functoriality conjecture. There has been a recent major development in the Langlands functoriality conjecture by the use of automorphic...
Springer, 2021. — 316 p. — ISBN 978-3-030-68489-1. This book gives its readers a unique opportunity to get acquainted with new aspects of the fruitful interactions between Analysis, Geometry, Quantum Mechanics and Number Theory. The present book contains a number of contributions by specialists in these areas as an homage to the memory of the mathematician Erik Balslev and, at...
Springer, 2021. — 316 p. — ISBN 978-3-030-68489-1. This book gives its readers a unique opportunity to get acquainted with new aspects of the fruitful interactions between Analysis, Geometry, Quantum Mechanics and Number Theory. The present book contains a number of contributions by specialists in these areas as an homage to the memory of the mathematician Erik Balslev and, at...
Singapore: World Scientific, 1993. — 130 p. The book is devoted to new and classical results of the theory of linear partial differential operators in Gevrey spaces. The “microlocal approach” is adopted, by using pseudo-differential operators, wave front sets and Fourier integral operators. Basic results for Schwartz-distributions, c∞ and analytic classes are also included,...
Berlin: de Gruyter, 2020. — 458 p. This authoritative text studies pseudodifferential and Fourier integral operators in the framework of time-frequency analysis, providing an elementary approach, along with applications to almost diagonalization of such operators and to the sparsity of their Gabor representations. Moreover, Gabor frames and modulation spaces are employed to...
Basel: Birkhäuser, 2021. — 270 p. — (Birkhäuser Advanced Texts Basler Lehrbücher). — ISBN 978-3-030-67461-8. This textbook provides a graduate-level introduction to the spectral theory of linear operators on Banach and Hilbert spaces, guiding readers through key components of spectral theory and its applications in quantum physics. Based on their extensive teaching experience,...
Basel: Birkhäuser, 2021. — 270 p. — (Birkhäuser Advanced Texts Basler Lehrbücher). — ISBN 978-3-030-67461-8. This textbook provides a graduate-level introduction to the spectral theory of linear operators on Banach and Hilbert spaces, guiding readers through key components of spectral theory and its applications in quantum physics. Based on their extensive teaching experience,...
Boston: de Gruyter, 2016. — 423 p. — (De Gruyter Studies in Mathematical Physics 35) — ISBN 978-3-11-043542-9. Invariant differential operators play a very important role in the description of physical symmetries – recall, e.g., the examples of Dirac, Maxwell, Klein–Gordon, d’Almbert, and Schrödinger equations. Invariant differential operators played and continue to play...
Basel: Birkhäuser, 1997. — 230 p. This book is devoted to the theory of entire operators, founded by one of the century's best known mathematicians, M.G. Krein. The theory lies at the junction of the spectral theory of Hermitian operators and the theory of analytic functions, harmoniously combining the methods of each. The purpose of the book is to show how various problems of...
Basel: Birkhäuser, 2000. — 425 p. The present book is the second of the two volume Proceedings of the Mark Krein International Conference on Operator Theory and Applications. This conference, which was dedicated to the 90th Anniversary of the prominent mathematician Mark Krein, was held in Odessa, Ukraine from 18-22 August, 1997. The conference focused on the main ideas,...
Basel: Birkhäuser, 2000. — 418 p. The present book is the first of the two volume Proceedings of the Mark Krein International Conference on Operator Theory and Applications. This conference, which was dedicated to the 90th Anniversary of the prominent mathematician Mark Krein, was held in Odessa, Ukraine from 18-22 August, 1997. The confer encefocused onthemain ideas, methods,...
М.: Наука, 1966. — 500 с. Многие задачи функционального анализа и математической физики требуют решения или исследования линейных и нелинейных интегральных уравнений. В связи с этим важную роль играет изучение различных классов интегральных операторов. В монографии проводится систематический анализ линейных и нелинейных интегральных операторов, устанавливаются общие признаки их...
Cambridge University Press, 2006. — 508 p. — (Cambridge studies in advanced mathematics 99). — ISBN-13 9780511221019. L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to...
Монография. — М.: Физматлит, 1962. — 327 с. Монография посвящена изложению теории операторов обобщенного сдвига и некоторых их применений. Операторами обобщенного сдвига (в дальнейшем сокращенно: о. о. с.) называются семейства операторов, зависящих от одного или нескольких параметров и удовлетворяющих аксиомам, обобщающим свойства обычного сдвига для функций.
New York: Springer, 2021. — 379 p. This book presents modern methods in functional analysis and operator theory along with their applications in recent research. The book also deals with the solvability of infinite systems of linear equations in various sequence spaces. It uses the classical sequence spaces, generalized Cesaro and difference operators to obtain calculations and...
Basel: Birkhäuser, 2021. — 337 p. This volume features selected papers from The Fifteenth International Conference on Order Analysis and Related Problems of Mathematical Modeling, which was held in Vladikavkaz, Russia, on 15 - 20th July2019. Intended for mathematicians specializing in operator theory, functional spaces, differential equations or mathematical modeling, the book...
New York: Academic Press, 1988. — 242 p. This book presents interpolation theory from its classical roots beginning with Banach function spaces and equimeasurable rearrangements of functions, providing a thorough introduction to the theory of rearrangement-invariant Banach function spaces. At the same time, however, it clearly shows how the theory should be generalized in order...
Springer, 2020. — 531 p. — (Operator Theory Advances and Applications 278). — ISBN 978-3-030-43379-6. This book is the proceeding of the International Workshop on Operator Theory and Applications (IWOTA) held in July 2018 in Shanghai, China. It consists of original papers, surveys and expository articles in the broad areas of operator theory, operator algebras and...
Boca Raton: CRC Press, 1987. — 610 p. This introduction to functional analysis focuses on the types of singularity that prevent an operator from being invertible. The presentation is based on the open mapping theorem, Hahn-Banach theorem, dual space construction, enlargement of normed space, and Liouville's theorem. Suitable for advanced undergraduate and graduate courses in...
De Gruyter, 2020. — 364 p. — (Advances in Analysis and Geometry 02). — ISBN: 978-3-11-065339-7. The fundamental contributions made by the late Victor Lomonosov in several areas of analysis are revisited in this book, in particular, by presenting new results and future directions from world-recognized specialists in the field. The invariant subspace problem, Burnside's theorem,...
London: ICP, 2005. — 504 p. This volume concentrates on how to construct a Markov process by starting with a suitable pseudo-differential operator. Feller processes, Hunt processes associated with Lp-sub-Markovian semigroups and processes constructed by using the Martingale problem are at the center of the considerations. The potential theory of these processes is further...
London: ICP, 2002. — 477 p. In this volume two topics are discussed: the construction of Feller and Lp-sub-Markovian semigroups by starting with a pseudo-differential operator, and the potential theory of these semigroups and their generators. The first part of the text essentially discusses the analysis of pseudo-differential operators with negative definite symbols and...
London: ICP, 2001. — 517 p. After recalling essentials of analysis — including functional analysis, convexity, distribution theory and interpolation theory — this book handles two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and...
New York: Springer, 2019. — 431 p. Foreword An Open Problem in Operator Theory Complementarity of Position and Momentum Further Developments of the Theory of Complementary Pairs n-Complementarity Tensor Algebras Over Vector Spaces Actions of H and H* on Tens(H) and Tenssym(H) Commutations Relations Interacting Fock Spaces Over a Semi-Hilbert Space -Mode Type IFS -Mode Type...
Basel: Birkhäuser, 1990. — 311 p. Realization and factorization for rational matrix functions with symmetries. Lossless inverse scattering and reproducing kernels for upper triangular operators. Zero-pole structure of nonregular rational matrix functions. Structured interpolation theory. Extension theorems for contraction operators on Krein spaces.
Cambridge: Cambridge University Press, 1997. — 335 p. The new Calderon-Zygmund operators David and Journe's T(1) theorem Examples of Calderon-Zygmund operators Operators corresponding to singular integrals: their continuity on Hoelder and Sobolev spaces The T(b) theorem Generalized Hardy spaces Multilinear operators Multilinear analysis of square roots of accretive operators...
Springer, 2020. — 459 p. — (Operator Theory: Advances and Applications, Volume 279). — ISBN: 978-3-030-44650-5. This book features a collection of up-to-date research papers that study various aspects of general operator algebra theory and concrete classes of operators, including a range of applications. Most of the papers included were presented at the International Workshop...
Монография. — М.: Московский государственный университет (МГУ) имени М.В. Ломоносова, 1996. — 59 с. Приведен ряд теорем типа Гельмана-Фейнмана, дающих удобные выражения для производных собственных значений самосопряженных операторов по параметрам, от которых зависят рассматриваемые операторы. Доказана теорема о том, что у полуограниченного снизу самосопряженного оператора,...
Springer, 2015. — 327 p. — (Lecture Notes in Mathematics 2145). — ISBN: 978-3-662-46844-9. This book deals with various aspects of commutants and reducing subspaces of multiplication operators on the Bergman space, along with relevant von Neumann algebras generated by these operators, which have been the focus of considerable attention from the authors and other experts in...
Cambridge: Cambridge University Press, 1987. — 361 p. The notion of "s-numbers" of an operator is designed to incorporate the approximation, Gelfand and Kolmogorov numbers; further examples are Weyl, Chang and Hilbert numbers. The emphasis here is on quasi-norms formed from the various sequences of s-numbers, and on their relationship with the summing norms. For operators...
New York: American Mathematical Society, 2000. — 199 p. Shift operators on Hilbert spaces of analytic functions play an important role in the study of bounded linear operators on Hilbert spaces since they often serve as models for various classes of linear operators. For example, “parts” of direct sums of the backward shift operator on the classical Hardy space H2 model certain...
Springer, 2020. — 422 p. — (Moscow Lectures 05). — ISBN: 978-3-030-42399-5 This book offers an introduction to the research in several recently discovered and actively developing mathematical and mathematical physics areas. It focuses on: 1) Feynman integrals and modular functions, 2) hyperbolic and Lorentzian Kac-Moody algebras, related automorphic forms and applications to...
Springer, 2020. — 446 p. — (Springer Proceedings in Mathematics & Statistics 325). — ISBN: 978-3-030-46078-5. This book features selected and peer-reviewed lectures presented at the 3rd Semigroups of Operators: Theory and Applications Conference, held in Kazimierz Dolny, Poland, in October 2018 to mark the 85th birthday of Jan Kisyński. Held every five years, the conference...
Bookboon, 2014. — 66 p. In this book you find the basic mathematics that is needed by engineers and university students . The author will help you to understand the meaning and function of mathematical concepts. The best way to learn it, is by doing it, the exercises in this book will help you do just that. Topics as Topological, metric, Hilbert and Banach spaces and Spectral...
Bookboon, 2014. — 109 p. In this book you find the basic mathematics that is needed by engineers and university students . The author will help you to understand the meaning and function of mathematical concepts. The best way to learn it, is by doing it, the exercises in this book will help you do just that. Topics as Topological, metric, Hilbert and Banach spaces and Spectral...
New York: Springer, 2020. — 685 p. Transmutation operators in differential equations and spectral theory can be used to reveal the relations between different problems, and often make it possible to transform difficult problems into easier ones. Accordingly, they represent an important mathematical tool in the theory of inverse and scattering problems, of ordinary and partial...
CRC Press, 1993. — 168 p. — (Studies in Advanced Mathematics). — ISBN13: 9781315137292. Focuses on the fundamental results in operator algebras. This work discusses results including Gelfand's representation of commutative C*-algebras, the GNS construction, the spectral theorem, polar decomposition, von Neumann's double commutant theorem, Kaplansky's density theorem and the...
Саратов: Саратовский государственный университет им. Н.Г. Чернышевского (СГУ), 2016. — 88 с. Во многих областях математики большое значение имеют задачи о приближении сложных объектов менее сложными. Теория приближений имеет дело главным образом с приближением отдельных функций из некоторого класса при помощи функций из некоторого множества, являющихся более простыми, чем...
Саратов: Саратовский государственный университет им. Н.Г. Чернышевского (СГУ), 2016. — 48 с. Линейные положительные операторы играют большую роль в теории приближения, поскольку обладают рядом простых свойств, облегчающих их изучение. В частности, для линейных положительных операторов наиболее просто формулируются условия, когда последовательность операторов сходится к...
Springer, 2020. — 339 p. — (Graduate Texts in Mathematics 284). — ISBN: 978-3-030-38001-4. This textbook offers a concise introduction to spectral theory, designed for newcomers to functional analysis. Curating the content carefully, the author builds to a proof of the spectral theorem in the early part of the book. Subsequent chapters illustrate a variety of application areas,...
Учебное пособие. — Москва: Макс Пресс, 2010. — 48 с. Учебное пособие представляет изложение основ теории полугрупп линейных ограниченных операторов в банаховых пространствах, а также ее приложения к решению абстрактных параболических задач. Введение Полугруппы линейных операторов Равномерно непрерывные полугруппы Сильно непрерывные полугруппы Решение задачи Коши методом полугрупп
New York: Springer, 1977. — 150 p. The asymptotic distribution of the eigen values of finite section Toeplitz operators as the section parameter increases to has been known ever since the fundamental paper of Szego, "Ein Gren£wertsatz uber die Toeplltzschen Determlnanten elner reellen positiven Funktion", Math. Ann. 76, 490-503 (1915). In the last fifteen years interest has been...
Springer, 2020. — 121 p. — (SpringerBriefsiIn Mathematics). — ISBN: 978-3-030-38311-4. This work contributes to the study of quaternionic linear operators. This study is a generalization of the complex case, but the noncommutative setting of quaternions shows several interesting new features, see e.g. the so-called S-spectrum and S-resolvent operators. In this work, we study de...
Basel: Birkhauser, 2020. — 257 p. This textbook introduces spectral theory for bounded linear operators by focusing on (i) the spectral theory and functional calculus for normal operators acting on Hilbert spaces; (ii) the Riesz-Dunford functional calculus for Banach-space operators; and (iii) the Fredholm theory in both Banach and Hilbert spaces. Detailed proofs of all theorems...
Sprringer, 2016. — 240 p. — (Operator Theory: Advances and Applications 255). — ISBN: 978-3-319-31381-8. This volume collects a selected number of papers presented at the International Workshop on Operator Theory and its Applications (IWOTA) held in July 2014 at Vrije Universiteit in Amsterdam. Main developments in the broad area of operator theory are covered, with special...
American Mathematical Society, 2019. — 100 p. — ISBN: 978-1-4704-3624-7; ISBN: 978-1-4704-5323-7. In this paper, the authors study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. They first establish a criterion on the coprime-ness of two singular inner functions and obtain several properties of the...
CRC Press, 2019. — 360 p. Handbook of Analytic Operator Theory thoroughly covers the subject of holomorphic function spaces and operators acting on them. The spaces covered include Bergman spaces, Hardy spaces, Fock spaces and the Drury-Averson space. Operators discussed in the book include Toeplitz operators, Hankel operators, composition operators, and Cowen-Douglas class...
Berlin: Springer, 1977. — 150 p. Hilbert space background — Small eigen values The fourier transform theorem The fourier series theorem Hilbert space theory — Large eigen values The fourier series and fourier transform theorems
Springer, 2015. — 131 p. — (Lecture Notes in Applied and Numerical Harmonic Analysis). — ISBN: 978-3-319-26679-4. In this set of lecture notes, the author includes some of the latest research on the theory of Morrey Spaces associated with Harmonic Analysis. There are three main claims concerning these spaces that are covered: determining the integrability classes of the trace...
UK: Birkhaueser, 2007. — 405 p. — (Operator Theory: Advances and Applications 171). — ISBN: 978-37643-79797. This volume contains contributions originating from the International Workshop on Operator Theory and Its Applications (IWOTA) held in Newcastle upon Tyne in July 2004. The articles expertly cover a broad range of material at the cutting edge of functional analysis and...
New York: Springer, 2019. — 307 p. Correspondences of Power Series Actions of SL(2,R) on Power Series Jacobi-like Forms and Modular Series Pseudodifferential Operators Power Series Bundles Automorphic Pseudodifferential Operators of Mixed Weight Bundles of Pseudodifferential Operators Poincaré Series Linear Maps and Rankin–Cohen Brackets Jacobi-like Forms, Modular Series, and...
New York: Springer, 2019. — 515 p. This book is an outcome of two Conferences on Ulam Type Stability (CUTS) organized in 2016 (July 4-9, Cluj-Napoca, Romania) and in 2018 (October 8-13, 2018, Timisoara, Romania). It presents up-to-date insightful perspective and very resent research results on Ulam type stability of various classes of linear and nonlinear operators; in...
Springer, 2019. — 102 p. — (Springer Briefs in Mathematics). — ISBN: 978-3-030-19454-3. This book is a valuable resource for Graduate students and researchers interested in current techniques and methods within the theory of moments in linear positive operators and approximation theory. Moments are essential to the convergence of a sequence of linear positive operators. Several...
Basel: Birkhäuser, 2008. — 339 p. This book expands the lectures given at IWOTA 05 (International Workshop on Operator Theory and Applications) which was held at the University of Connecticut, Storrs, USA, July 24 27, 2005. Many developments on the cutting edge of research in operator theory, matrix theory, coding theory, system theory, control theory and numerical linear...
Монография. — Владивосток: Дальневосточное отделение Российской академии наук (ДВО РАН), 2000. — 80 с. Книга посвящена задаче об интегральности произведений операторов , в которых по крайней мере один из сомножителей — интегральный оператор. Устанавливаются различные условия интегральности таких произведений. Характеризуются состоящие из интегральных либо частично интегральных...
2nd Edition. — Springer, 1998. — 212 p. — (Graduate Texts in Mathematics 179). — ISBN: 978-0-387-98377-6. Operator theory is a diverse area of mathematics which derives its impetus and motivation from several sources. It began with the study of integral equations and now includes the study of operators and collections of operators arising in various branches of physics and...
Birkhäuser, Springer, 2010. — 447 p. — (Operator Theory: Advances and Applications 203). — ISBN: 978-3-0346-0160-3. This is the second volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory...
Birkhäuser, Springer, 2010. — 624 p. — (Operator Theory: Advances and Applications 202). — ISBN: 978-3-0346-0157-3. The present volume is the first of two volumes containing a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical...
Springer, 2010. — 540 p. — (Operator Theory: Advances and Applications 217). — ISBN: 978-3-7643-9995-5. This book is devoted to conservative realizations of various classes of Stieltjes, inverse Stieltjes, and general Herglotz-Nevanlinna functions as impedance functions of linear systems. The main feature of the monograph is a new approach to the realization theory profoundly...
Cambridge University Press, 2019. — 236 p. — (London Mathematical Society Student Texts, 93). — ISBN: 978-1-108-48309-4. The theory of semigroups of operators is one of the most important themes in modern analysis. Not only does it have great intellectual beauty, but also wide-ranging applications. In this book the author first presents the essential elements of the theory,...
New York: Nova Science Publishers, 2009. — 134 p. — ISBN: 1606928864. This book is devoted to the measure of non-compactness (essential norm) in weighted Lebesgue spaces for maximal, potential and singular operators dened, generally speaking, on homogeneous groups. The main topics of the monograph contain related results for potential and singular integrals in weighted function...
Dordrecht: Kluwer, 1990. — 299 p. The Weyl-Hoermander Calculus of Pseudodifferential Operators. Classes of Symbols. Estimates for Solutions of Schroedinger-Type Equations. The Fundamental Theorems of Calculus. Continuity of Pseudodifferential Operators. Weight Spaces of Sobolev Type. Action of Pseudodifferential Operators in Weight Spaces. Basic Theorems of the Method of...
Basel: Birkhäuser, 2009. — 536 p. This is the second of two volumes containing peer-reviewed research and survey papers based on invited talks at the International Conference on Modern Analysis and Applications. The conference, which was dedicated to the 100th anniversary of the birth of Mark Krein, one of the greatest mathematicians of the 20th century, was held in Odessa,...
Basel: Birkhäuser, 2009. — 513 p. This is the first of two volumes containing peer-reviewed research and survey papers based on invited talks at the International Conference on Modern Analysis and Applications. The conference, which was dedicated to the 100th anniversary of the birth of Mark Krein, one of the greatest mathematicians of the 20th century, was held in Odessa,...
Springer, 2019. — 419 p. — (Springer Optimization and Its Applications 146). — ISBN: 978-3-030-12660-5. Dedicated to Tosio Kato’s 100th birthday, this book contains research and survey papers on a broad spectrum of methods, theories, and problems in mathematics and mathematical physics. Survey papers and in-depth technical papers emphasize linear and nonlinear analysis,...
Springer, 2019. — 488 p. — ISBN: 303010818X. The asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more than a century ago. In the last decades there has been a renewed interest in non-self-adjoint differential operators which have many subtle...
Монография. — Москва; Санкт-Петербург; Киев: Диалектика, 2009. — 185 с. По мнению авторов в данной книге найдены основные элементы общего подхода к построению теории общей разрешимости операторных уравнений. Первая глава содержит основные определения и вспомогательные факты. Во второй главе даны описания простейших схем обобщенного решения в случае линейных операторов. В третьей...
New York: Springer, 2018. — 373 p. This monograph offers a self-contained introduction to pseudodifferential operators and wavelets over real and p-adic fields. Aimed at graduate students and researchers interested in harmonic analysis over local fields, the topics covered in this book include pseudodifferential operators of principal type and of variable order, semilinear...
Springer, 2019. — 390 p. — (Operator Theory: Advances and Applications 272). — ISBN: 3030116131. This volume is devoted to Joseph A. (Joe) Ball’s contributions to operator theory and its applications and in celebration of his seventieth birthday. Joe Ball’s career spans over four and a half decades, starting with his work on model theory and related topics for non-contractions...
American Mathematical Society, 2008. — 168 p. — (Translations of Mathematical Monographs 237). — ISBN: 0821839470. In the early 1980's topologists and geometers for the first time came across unfamiliar words like C-algebras and von Neumann algebras through the discovery of new knot invariants (by V. F. R. Jones) or through a remarkable result on the relationship between...
Springer, 2018. — 499 p. — (Operator Theory Advances and Applications 271). — ISBN: 978-3-030-04268-4. This volume is dedicated to Rien Kaashoek on the occasion of his 80th birthday and celebrates his many contributions to the field of operator theory during more than fifty years. In the first part of the volume, biographical information and personal accounts on the life of...
Oakville (Can.): Apple Academic Press Inc., 2018. — 368 p. — ISBN: 978-1-351-04627-5. This book is intended to provide a fairly comprehensive study of spectral theory of linear operators defined on Banach spaces. The central items of interest include various essential spectra, but we also consider some of their generalizations that have been studied in recent years. As the...
Springer, 2019. — 287 p. — ISBN: 3030026469. This book introduces the peridynamic (PD) differential operator, which enables the nonlocal form of local differentiation. PD is a bridge between differentiation and integration. It provides the computational solution of complex field equations and evaluation of derivatives of smooth or scattered data in the presence of...
Paris: European Mathematical Society, 2019. — 264 p. Inequalities for differential operators play a fundamental role in the modern theory of partial differential equations. Among the numerous applications of such inequalities are existence and uniqueness theorems, error estimates for numerical approximations of solutions and for residual terms in asymptotic formulas, as well as...
Springer, 2018. — 248 p. — ISBN: 981133076X. This book discusses the Tauberian conditions under which convergence follows from statistical summability, various linear positive operators, Urysohn-type nonlinear Bernstein operators and also presents the use of Banach sequence spaces in the theory of infinite systems of differential equations. It also includes the generalization...
Springer, 2018. — 248 p. — ISBN: 981133076X. This book discusses the Tauberian conditions under which convergence follows from statistical summability, various linear positive operators, Urysohn-type nonlinear Bernstein operators and also presents the use of Banach sequence spaces in the theory of infinite systems of differential equations. It also includes the generalization...
De Gruyter, 2018. — 229 p. — (Studies in Mathematical Physics 49). — ISBN: 3110526638. The De Gruyter Studies in Mathematical Physics are devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand,...
Boston: de Gruyter, 2016. — 423 p. Invariant differential operators play a very important role in the description of physical symmetries – recall, e.g., the examples of Dirac, Maxwell, Klein–Gordon, d’Almbert, and Schrödinger equations. Invariant differential operators played and continue to play important role in applications to conformal field theory. Invariant superdifferential...
Препринт. — Новосибирск: Институт математики СО АН СССР, 1981. — 48 с. С помощью аппарата квазирезольвенты дается описание производящих операторов равномерно суммируемых (в нуле) однопараметрических полугрупп линейных непрерывных операторов, действующих в локально выпуклом пространстве.
Монография. — М.: Наука, 1973. — 312 с. Монография посвящена изложению теории операторов обобщенного сдвига и некоторых их применений. Операторами обобщенного сдвига (в дальнейшем сокращенно: о. о. с.) называются семейства операторов, зависящих рт одного или нескольких параметров и удовлетворяющих аксиомам, обобщающим свойства обычного сдвига для функций. Основное внимание в...
Philadelphia: Society for Industrial & Applied Mathematics, 2011. — 382 p. This classic textbook provides a unified treatment of spectral approximation for closed or bounded operators as well as for matrices. Despite significant changes and advances in the field since it was first published in 1983, the book continues to form the theoretical bedrock for any computational...
USA: Kluwer Academic Publishers, Springer, 2004. — 452 p. A signi?cant sector of the development of spectral theory outside the classical area of Hilbert space may be found amongst at multipliers de?ned on a complex commutative Banach algebra A. Although the general theory of multipliers for abstract Banach algebras has been widely investigated by several authors, it is...
Springer, 2018. — 552 p. — (Lecture Notes in Mathematics 2235). — ISBN: 978-3-030-02265-5. This monograph concerns the relationship between the local spectral theory and Fredholm theory of bounded linear operators acting on Banach spaces. The purpose of this book is to provide a first general treatment of the theory of operators for which Weyl-type or Browder-type theorems...
Berlin: Springer, 2014. — xx + 552 p. — (Grundlehren der mathematischen Wissenschaften 348). — ISBN: 978-3-319-00227-9. The present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curvature properties of the underlying structure in order to study convergence to equilibrium, spectral bounds,...
Springer, 2018. — 89 р. — (SpringerBriefs in Mathematics). — ISBN: 3319942913. The purpose of this Brief is to give a quick practical introduction into the subject of Toeplitz operators on Kähler manifolds, via examples, worked out carefully and in detail. Necessary background is included. Several theorems on asymptotics of Toeplitz operators are reviewed and illustrated by...
Springer, 2018. — 200 p. — (Compact Textbooks in Mathematics). — ISBN: 331992060X. The book concisely presents the fundamental aspects of the theory of operators on Hilbert spaces. The topics covered include functional calculus and spectral theorems, compact operators, trace class and Hilbert-Schmidt operators, self-adjoint extensions of symmetric operators, and one-parameter...
Springer, 2018. — 374 p. — (Applied and Numerical Harmonic Analysis). — ISBN: 978-3-319-65321-1. This text is a self-contained introduction to the three main families that we encounter in analysis – metric spaces, normed spaces, and inner product spaces – and to the operators that transform objects in one into objects in another. With an emphasis on the fundamental properties...
New York: Springer, 2018. — 408 p. — ISBN: 978-3-319-93501-0. This self-contained monograph presents an overview of fuzzy operator theory in mathematical analysis. Concepts, principles, methods, techniques, and applications of fuzzy operator theory are unified in this book to provide an introduction to graduate students and researchers in mathematics, applied sciences, physics,...
Cambridge University Press, 2007. — 465 p. — ISBN13: 978-0-511-28503-5. This wide ranging but self-contained account of the spectral theory of non-self-adjoint linear operators is ideal for postgraduate students and researchers, and contains many illustrative examples and exercises. Fredholm theory, Hilbert-Schmidt and trace class operators are discussed, as are one-parameter...
Springer, 2018. — 145 p. — (SpringerBriefs in Mathematical Physics 32). — ISBN: 978-3-319-94754-9. Refection Positivity is a central theme at the crossroads of Lie group representations, euclidean and abstract harmonic analysis, constructive quantum field theory, and stochastic processes. This book provides the first presentation of the representation theoretic aspects of...
Springer, 2013. — 167 p. — (Pseudo-Differential Operators. Theory and Applications 09). – ISBN: 97830348-02932. The concept of associating ordinary functions with operators has arisen in many areas of science and mathematics and it can be argued that the earliest instance was Leibniz’s attempt to define a fractional derivative. Up to the beginning of the twentieth century, many...
Basel: Birkhäuser, 2018. — 506 p. This book presents 29 invited articles written by participants of the International Workshop on Operator Theory and its Applications held in Chemnitz in 2017. The contributions include both expository essays and original research papers illustrating the diversity and beauty of insights gained by applying operator theory to concrete problems. The...
Springer, 2015. — 208 p. — (Pseudo-Differential Operators: Theory and Applications 11). — ISBN: 978-3-319-18656-6. The main results of this book combine pseudo differential analysis with modular form theory. The methods rely for the most part on explicit spectral theory and the extended use of special functions. The starting point is a notion of modular distribution in the...
Монография. — М.: Московский государственный университет печати (МГУП), 2010. — 496 с. — ISBN: 978-5-8122-1076-2. Во второй части монографии продолжается исследование сингулярных операторов Штурма—Лиувиля, действующих в функциональных гильбертовых пространствах с индефинитной метрикой. Исследование опирается на материал монографии автора «Обобщенно-классические ортогональные...
Монография. — М.: Московский государственный университет печати (МГУП), 2010. — 496 с. — ISBN: 978-5-8122-1076-2. Во второй части монографии продолжается исследование сингулярных операторов Штурма—Лиувиля, действующих в функциональных гильбертовых пространствах с индефинитной метрикой. Исследование опирается на материал монографии автора «Обобщенно-классические ортогональные...
Монография. — М.: Московский государственный университет печати (МГУП), 2010. — 504 с. — ISBN: 978-5-8122-1076-2. В монографии исследуются сингулярные операторы Штурма—Лиувилля, действующие в функциональных гильбертовых пространствах с индефинитной метрикой. Исследование опирается на материал монографии автора «Обобщенно-классические ортогональные многочлены». Для научных...
Монография. — М.: Московский государственный университет печати (МГУП), 2010. — 504 с. — ISBN: 978-5-8122-1076-2. В монографии исследуются сингулярные операторы Штурма—Лиувилля, действующие в функциональных гильбертовых пространствах с индефинитной метрикой. Исследование опирается на материал монографии автора «Обобщенно-классические ортогональные многочлены». Для научных...
Учебное пособие. — Екатеринбург: Уральский федеральный университет имени первого президента России Б.Н. Ельцина (УрФУ), 2018. — 128 с. — ISBN: 978-5-7996-2306-7. В учебном пособии рассматриваются вопросы функционального анализа, не вошедшие в общий курс функционального анализа по программе бакалавриата, в частности спектральное представление самосопряженных операторов (как...
Монография. — М.: Иностранная литература, 1951. — 636 с. Книга американского математика Эйнара Хилле (изначально его фамилия была транскрипирована как Хилл) является первой монографией по теории полугрупп операторов (американское издание 1948 года), одним из важнейших для приложений разделов функционального анализа. Изложение функционального анализа в этой книге ведётся,...
Tokyo: Mathematical Society of Japan, 2000. — 93 p. This note is based on series of lectures presented by Prof. Eric M. Opdam in one of the workshops of the Research Project “Harmonic analysis on homogeneous spaces and represenattion of Lie groups” at RIMS Kyoto University in 1997. The first part is an exposition of Dunkl operators in the trigonometric, differential setting...
Clarendon Press, 2004. — 398 p. This invaluable reference is the first to present the general theory of algebras of operators on a Hilbert space, and the modules over such algebras. The new theory of operator spaces is presented early on and the text assembles the basic concepts, theory and methodologies needed to equip a beginning researcher in this area. A major trend in modern...
Birkhauser, 2008. — 443 p. This book is composed of three survey lecture courses and nineteen invited research papers presented to WOAT 2006 - the International Summer School and Workshop on Operator Algebras, Operator Theory and Applications, which was held at Lisbon in September 2006. The volume reflects recent developments in the area of operator algebras and their interaction...
Springer, 2013. — 134 p. This volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum theory. The author, a leading authority on the subject, sets out numerous results previously...
Birkhauser, 1992. — 603 p. This volume is the companion volume to Fundamentals of the Theory of Operator Algebras. Volume II—Advanced Theory (Graduate Studies in Mathematics series, Volume 16). The goal of the text proper is to teach the subject and lead readers to where the vast literature—in the subject specifically and in its many applications—becomes accessible. The choice of...
Birkhauser, 1991. — 284 p. This volume is the companion volume to Fundamentals of the Theory of Operator Algebras, Volume II - Advanced Theory (Graduate Studies in Mathematics series, Volume 16). The goal of the text proper is to teach the subject and lead readers to where the vast literature - in the subject specifically and in its many applications - becomes accessible. The...
Springer International Publishing AG, 2017. — 152 p. — (Lecture Notes in Mathematics 2199) — ISBN: 3319658093. This book exploits the classification of a class of linear bounded operators with rank-one self-commutators in terms of their spectral parameter, known as the principal function. The resulting dictionary between two dimensional planar shapes with a degree of shade and...
Томск: Томский государственный университет, 2007. — 364 с. — ISBN: 5-94621-224-9. В монографии анализируется алгебра экспоненциальных гипергеометрических операторов сдвига, которые в наиболее важных случаях являются представлениями известных групп. Выделены особые алгебраические соотношения и тождества между экспонентами от операторов сдвига различного типа. Построенные основы...
Учебное пособие. — 2-е изд., испр. и доп. — СПб.: Лань, 2010. — 464 с.— (Учебники для вузов. Специальная литература). — ISBN: 978-5-8114-1076-7. Эта книга вышла первым изданием в 1980 г. и сразу стала библиографической редкостью. Настоящее издание значительно расширено: в него внесены многочисленные добавления, подготовленные для английского перевода, опубликованного в 1987 г....
Монография. — М.: Наука, 1973. — 312 с. Монография посвящена изложению теории операторов обобщенного сдвига и некоторых их применений. Операторами обобщенного сдвига (в дальнейшем сокращенно: о. о. с.) называются семейства операторов, зависящих рт одного или нескольких параметров и удовлетворяющих аксиомам, обобщающим свойства обычного сдвига для функций. Основное внимание в...
Springer, 2006. — 248 p. — (Universitext). The theory of strongly continuous semigroups of linear operators on Banach spaces, operator semigroups for short, has become an indispensable tool in a great number of areas of modern mathematical analysis. In our Springer Graduate Text [EN00] we presented this beautiful theory, together with many applications, and tried to show the...
Birkhauser, 2010. — 314 p. The present book is a memorial volume devoted to Peter Jonas. It displays recent advances in modern operator theory in Hilbert and Krein spaces and contains a collection of original research papers written by many well-known specialists in this field. The papers contain new results for problems close to the area of research of Peter Jonas: Spectral and...
Providence: American Mathematical Society, 2006. — 83 p. We define a new notion of entropy for operators on Fock spaces and positive multi-Toeplitz kernels on free semigroups. This is studied in connection with factorization theorems for (e.g., multi-Toeplitz, multi-analytic, etc.) operators on Fock spaces. These results lead to entropy inequalities and entropy formulas for...
Walter de Gruyter, 2003. — 215 p. In 1903 Fredholm published his famous paper on integral equations. Since then linear integral operators have become an important tool in many areas, including the theory of Fourier series and Fourier integrals, approximation theory and summability theory, and the theory of integral and differential equations. As regards the latter, applications...
Walter de Gruyter, 2004. — 421 p. In view of the eminent importance of spectral theory of linear operators in many fields of mathematics and physics, it is not surprising that various attempts have been made to define and study spectra also for nonlinear operators. This book provides a comprehensive and self-contained treatment of the theory, methods, and applications of nonlinear...
Springer, 1973. — 289 p. What do the words "nonlinear spectral theory" really mean? We can say that the subject of this theory includes the investigation o f such problems concerning nonlinear operators which, in the linear case, belong to the linear spectral theory. These lecture notes deal with two groups of problems the study of which has come near to some final results even...
Springer, 1976. — 242 p. This volume contains lecture notes for the five series of lectures at the Summer School on Nonlinear Operators and the Calculus of Variations, held at the Universite Libre de Bruxelles, September 8 to 19 1975. A Seminar program was organized concurrently with the School. We assume that the Seminar Speakers will publish their results on their own...
Israel Program for Scientific Translations, 1965. — 244 p. This monograph presents an account of the bases anddevelopment of direct methods for investigating the nature of the spectrum of singular differential operators. It bears upon periodical literature on the subject that has appeared over the last ten to fifteen years. The operator mainly considered is the Schroedinger...
Birkhauser, 1992. — 417 p. Workshop on Operator Theory and Complex Analysis Sapporo (Japan) June 1991. Scattering Matrices for Micro Schemes Vadim Adamyan Holomorphic Operators Between Krein Spaces and the Number of Squares of Associated Kernels D. Alpay, A. Dijksma, J. van der Ploeg, H. S. V. de Snoo On Reproducing Kernel Spaces, The Schur Algorithm, and Interpolation in a...
Birkhauser, 2011. — 182 p. This volume contains the proceedings of the OTAMP 2008 (Operator Theory, Analysis and Mathematical Physics) conference held at the Mathematical Research and Conference Center in Bedlewo near Poznan. It is composed of original research articles describing important results presented at the conference, some with extended review sections, as well as...
Springer, 1974 — 358 p. The book is based on lecture notes for a one-year course, addressed to general mathematics students at the second year graduate level, which I have offered on three occasions. {Twice at the University of Iowa (1961-62, 1965-66), once at the University of Texas (1969-70)}. I helped myself to generous portions of expositions I have admired. These include a...
Birkhauser, 2007. — 260 p. This volume contains lectures delivered by the participants of the international conference "Operator Theory, Analysis and Mathematical Physics" (OTAMP 2004), held at the Mathematical Research and Conference Center in Bedlewo near Poznan, Poland on July 6-11, 2004. The idea behind these lectures was to present interesting ramifications of operator...
Elsevier, 2005. — 443 p. Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations)....
Springer, 2006. — 672 p. Since the late 1980s, Toeplitz operators and matrices have remained a field of extensive research and the development during the last nearly twenty years is impressive. One encounters Toeplitz matrices in plenty of applications on the one hand, and Toeplitz operators confirmed their role as the basic elementary building blocks of more complicated operators...
Birkhauser, 2007. — 330 p. This volume contains six peer-refereed articles written on the occasion of the workshop "Operator theory, system theory and scattering theory: multidimensional generalizations and related topics", held at the Ben-Gurion University of the Negev from June 26 to July 1, 2005. The contributions which both survey their respective fields and contain new...
Тексти лекцій. — Львів: Львівський національний університет імені Івана Франка (ЛНУ), 2005. — 221 с. Розглянуто питання курсу функціонального аналізу, основні принципи лінійного функціонального аналізу, теорію обмежених і необмежених лінійних операторів і функціоналів у гільбертових просторах. Для студентів старших курсів математичних факультетів, а також для аспірантів.
Монография. — Киев: Наукова думка, 1983. — 212 с. В монографии освещены вопросы теории линейных операторов, преимущественно в гильбертовом пространстве. Наряду с общими вопросами теории рассмотрены различные методы построения спектральных разложений, связь с вариационными задачами (принцип максимума Понтрягина для линейных систем с бесконечным числом степеней свободы),...
Providence: American Mathematical Society, 1998. — 92 p. We study two operators which are sums of squares of analytic vector fields. By reducing to an ordinary differential operator, we will show the existence of nonlinear eigenvalues, which will be used to disprove analytic-hypoellipticity of the original operators.
Walter de Gruyter GmbH, Berlin, Boston, 2017. — 409 p. — (De Gruyter Studies in Mathematical Physics 39) — ISBN10: 3110435438. This is volume 2 of our trilogy on invariant differential operators. In volume 1 we presented our canonical procedure for the construction of invariant differential operators and showed its application to the objects of the initial domain – noncompact...
Apple Academic Press, 2017. — 477 p. — ISBN10: 1771885343, 13 978-1771885348. This new volume shows how it is possible to further develop and essentially extend the theory of operators in infinite-dimensional vector spaces, which plays an important role in mathematics, physics, information theory, and control theory. The book describes new mathematical structures, such as...
Springer International Publishing AG, 2017. — 418 p. — (Developments in Mathematics 49) — ISBN: 3319577611. This unique book explores the world of q, known technically as basic hypergeometric series, and represents the author's personal and life-long study-inspired by Ramanujan-of aspects of this broad topic. While the level of mathematical sophistication is graduated, the book...
Academic Press, 2016. — 74 p. — ISBN: 978-0-12-805346-1. This book provides a comprehensive discussion of the random norm of random bounded linear operators, also providing important random norms as random norms of differentiation operators and integral operators. After providing the basic definition of random norm of random bounded linear operators, the book then delves into...
Springer, 2017. — 176 p. — (Texts and Readings in Mathematics). — ISBN: 978-981-10-4864-7. The book presents major topics in semigroups, such as operator theory, partial differential equations, harmonic analysis, probability and statistics and classical and quantum mechanics, and applications. Along with a systematic development of the subject, the book emphasises on the...
Philadelphia: American Mathematical Society, 1999. — 175 p. This book is intended for graduate students and research mathematicians interested in operator theory, functional analysis, and vector lattices
Springer International Publishing AG, 2017. — 193 p. — (Developments in Mathematics 50). — ISBN: 3319587943. This book presents a systematic overview of approximation by linear combinations of positive linear operators, a useful tool used to increase the order of approximation. Fundamental and recent results from the past decade are described with their corresponding proofs....
Philadelphia: American Mathematical Society, 2007. — 179 p. This book presents two essential and apparently unrelated subjects. The first, microlocal analysis and the theory of pseudo-differential operators, is a basic tool in the study of partial differential equations and in analysis on manifolds. The second, the Nash-Moser theorem, continues to be fundamentally important in...
Paris: Société mathématique de France, 2017. - 122 p. This monograph is devoted to the dynamics on Sobolev spaces of the cubic Szegő equation on the circle ^1, equation* i_t u=(u^2u). equation* Here denotes the orthogonal projector from L^2(^1) onto the subspace L^2_+(^1) of functions with nonnegative Fourier modes. We construct a nonlinear Fourier transformation on...
Amsterdam: Springer, 2002. — 563 p. This book concentrates on the branching solutions of nonlinear operator equations and the theory of degenerate operator-differential equations especially applicable to algorithmic analysis and nonlinear PDE's in mechanics and mathematical physics. The authors expound the recent result on the generalized eigen-value problem, the perturbation...
New York: Springer, 2014. — 368 p. The study of linear positive operators is an area of mathematical studies with significant relevance to studies of computer-aided geometric design, numerical analysis, and differential equations. This book focuses on the convergence of linear positive operators in real and complex domains. The theoretical aspects of these operators have been an...
New York: Chapman and Hall/CRC, 2017. — 237 p. This book deals with the determinants of linear operators in Euclidean, Hilbert and Banach spaces. Determinants of operators give us an important tool for solving linear equations and invertibility conditions for linear operators, enable us to describe the spectra, to evaluate the multiplicities of eigenvalues, etc. We derive upper...
Монография. — Саарбрюкен: Palmarium, 2013. — 181 с. Монография посвящена важному для приложений разделу функционального анализа. В топологических пространствах последовательностей, составленных из элементов фиксированного банахова пространствах и функций, принимающих значения в этом пространстве, изучаются дискретный оператор Винера-Хопфа и связанный с ним оператор Теплица....
Учебное пособие. — Новосибирск: Новосибирский государственный университет (НГУ), 1972. — 184 с. Эта книжка представляет собой текст лекций, читавшихся в НГУ в 1969-1970 учебном году. Возникнув из линейной алгебры и из теории дифференциальных уравнения, функциональный анализ систематизирует, обобщает и развивает методы решения различных задач из этих областей классической...
Springer International Publishing, 2016. — 140 p. — (Springer Briefs in Mathematical Physics 14). — ISBN: 978-3-319-47702-2, 978-3-319-47701-5. This book gives a complete classification of all algebras with the Kadison-Singer property, when restricting to separable Hilbert spaces. The Kadison-Singer property deals with the following question: given a Hilbert space H and an...
Учебник для вузов с углубленным изучением математики. — 5-е изд., стереотип. — М.: Дрофа, 2004. — 384 с. — (Классический университетский учебник). — ISBN: 5-7107-8699-3. Учебник (4-е изд. — 2001 г.) соответствует программе курсов «Функциональный анализ», «Теория операторов», «Анализ III», которые читаются в университетах и педагогических вузах. В книге приведены основные...
Basel: Birkhäuser, 2016. — 237 p. — (Operator Theory: Advances and Applications 253). — ISBN: 978-3-319-29535-0; 978-3-319-29533-6.
This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which...
Basel: Birkhäuser, 2016. — 1003 p. — (Operator Theory: Advances and Applications 249). — ISBN: 978-3-319-21018-6; 978-3-319-21017-9. This book, the result of the authors’ long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis...
Basel: Birkhäuser, 2016. — 567 p. — (Operator Theory: Advances and Applications 248). — ISBN: 978-3-319-21015-5; 978-3-319-21014-8.
This book, the result of the authors' long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis...
New York: Springer. 2016. - 113 p.
Serves as a primer on the theory of bounded linear operators on separable Hilbert space
Presents the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus
Discusses a proof without digressing into a course on the Gelfand theory of commutative Banach algebras
Introduces the reader to the...
Монография. — Москва: Иностранная литература, 1951. — 636 с. Книга американского математика Эйнара Хилле (изначально его фамилия была транскрипирована как Хилл) является первой монографией по теории полугрупп операторов (американское издание 1948 года), одним из важнейших для приложений разделов функционального анализа. Изложение функционального анализа в этой книге ведётся,...
Учебное пособие. — Омск: Омский государственный университет (ОмГУ), 1988. — 39 с. Пособие предназначено для студентов, изучающих функциональный анализ. Теория векторных (линейных) пространств излагается с точки зрения функционального анализа (ограничений на размерность пространств нет). Задания и упражнения располагаются в последовательности, позволяющей без особых затруднений...
Монография. — М.: Московский государственный университет имени М.В. Ломоносова (МГУ), 1984. — 24 с. В настоящей работе проведено детальное изучение дискретного спектра оператора энергии Н системы трех частиц в специальном случае, когда начало непрерывного спектра совпадает с энергией трехчастичного распада системы. Для изучения дискретного спектра оператора Шредингера...
Учебное пособие. — М.: Московский государственный университет имени М.В. Ломоносова (МГУ), 1973. — 154 с. Эти лекции были прочитаны автором в 1972 году на механико-математическом факультете МГУ для преподавателей вузов страны, слушателей факультета повышения квалификации. В лекциях мы стремились с одной стороны, изложить основополагающий материал классического функционального...
М.: Наука, 1966. — 298 с.
В теории операторов связь между математикой и физикой всегда была особенно плодотворной, а в квантовой механике даже необходимой. Однако недавно возникшая и получившая большое развитие новая область функционального анализа — теория несамосопряженных операторов, почти не имела выхода в физику.
Цель книги — устранить указанный недостаток. В ней...
Учебное пособие. — Владикавказ: Владикавказский научный центр Российской академии наук, 2001. — 92 с. В учебном пособии изучаются операторы, действующие в векторных решетках или решеточно нормированных пространствах и сохраняющие отношение дизъюнктности. Рассмотрен также двойственный класс разложимых операторов. Основное внимание уделено вопросам порядковой ограниченности,...
Учебное пособие. — Владикавказ: Владикавказский научный центр Российской академии наук, 2001. — 111 с. Учебное пособие посвящено основам теории положительных операторов в векторных решетках. Основное внимание уделено вопросам продолжения и разложения положительных операторов, а также некоторым структурным свойствам различных классов порядково ограниченных операторов. Пособие...
Basel: Birkhauser, 2010. - 432p.
The present book deals with canonical factorization of matrix and operator functions that appear in state space form or that can be transformed into such a form. A unified geometric approach is used. The main results are all expressed explicitly in terms of matrices or operators, which are parameters of the state space representation. The...
Birkhäuser Verlag, P.O. Box 133, CH-4010 Basel, Switzerland, 2005. –298 p. – ISBN10: 3-7643-7145-5. This book is an expanded version of talks and contributed papers presented at a conference held at the University of California at Santa Barbara in March 2003, to celebrate the 75th birthday of Professor Harold S. Shapiro. The main theme of the conference was Quadrature Domains...
New York: Academic Press, 1986. — 693 p.
The primary purpose of this book is to teach, and to enable readers to study the recent literature on this subject and its many applications. It is suitable for graduate-level courses in functional analysis and operator algebras, and as a reference for self-study by graduates.
New York:Springer,1982. - 162 pages Chapter One Operator theory in finite-dimensional vector spaces Chapter Two Perturbation theory in a finite-dimensional space
Heldelberg: Springer, 1975. — 376 p. Propagation des singularites des solutions d’equations analogues a l’equation de Schrödinger. On the spectrum of positive elliptic operators and periodic bicharacteristics. Clean intersection theory and Fourier Integrals. Non-uniqueness for the Cauchy Problem. Solutions asymptotiques et groupe symplectique. Le polynome de Bernstein d’une...
New York: Academic Press, 1983. — 398 p.
The primary purpose of this book is to teach, and to enable readers to study the recent literature on this subject and its many applications. It is suitable for graduate-level courses in functional analysis and operator algebras, and as a reference for self-study by graduates.
Springer-Verlag, 2006. — 528 p.
This book offers a comprehensive introduction to the general theory of C*-algebras and von Neumann algebras. Beginning with the basics, the theory is developed through such topics as tensor products, nuclearity and exactness, crossed products, K-theory, and quasidiagonality. The presentation carefully and precisely explains the main features of...
Препринт. — Новосибирск: Институт математики СО АН СССР, 1981. — 48 с. С помощью аппарата квазирезольвенты дается описание производящих операторов равномерно суммируемых (в нуле) однопараметрических полугрупп линейных непрерывных операторов, действующих в локально выпуклом пространстве.
N.-Y.: CRC Press, 2001. — 272 p.
Most books on linear operators are not easy to follow for students and researchers without an extensive background in mathematics. Self-contained and using only matrix theory, Invitation to Linear Operators: From Matricies to Bounded Linear Operators on a Hilbert Space explains in easy-to-follow steps a variety of interesting recent results on...
Basel: Bärkhauser Verlag. – 2006. – 314 p. This volume contains papers written by the participants of the 3rd Workshop on Operator Theory in Krein spaces and Nonlinear Eigenvalue Problems, held at the Technische Universit.at Berlin, Germany, December 12 to 14, 2003. The workshop covered topics from spectral, perturbation and extension theory of linear operators in Krein spaces....
New York: Academic Press, 1972. – 228 p. Operator theory is a diverse area of mathematics which derives its impetus and motivation from several sources. It began as did practically all of modern analysis with the study of integral equations at the end of the last century. It now includes the study of operators and collections of operators arising in various branches of physics...
Publisher: Birkhäuser; 2012 edition (June 7, 2012), Hardcover: 197 pages, ISBN10: 0817683275 ISBN13: 978-0817683276 This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern introductory textbook for a first graduate course in the subject. The...
Publisher: Birkhäuser; 2nd ed. 2011 edition (March 9, 2011), Hardcover: 553 pages, ISBN10: 0817649972 ISBN13: 978-0817649975 This second edition of Elements of Operator Theory is a concept-driven textbook that includes a significant expansion of the problems and solutions used to illustrate the principles of operator theory. Written in a user-friendly, motivating style intended...
Amsterdam: North-Holland. - 1987. - 246 p. (North-Holland Mathematical Library. Vol. 38) The present book contains the basics of the algebra of operators. It is devoted to the study of so-called linear operators, which corresponds to that of the linear forms аг+ a2x2 + . + anxn of algebra. In this book, I have elected, above all, to gather together results concerning linear...
World Scientific Publishing, 1992. — 750 pages. ISBN: 981020941X
This book is an introductory text on one of the most important fields of mathematics, the theory of operator algebras. It offers a readable exposition of the basic concepts, techniques, structures and important results of operator algebras. Written in a self-contained manner, with an emphasis on understanding, it...
Springer, 2013. — 265 pages. ISBN: 1461469457
The approximation of functions by linear positive operators is an important research topic in general mathematics and it also provides powerful tools to application areas such as computer-aided geometric design, numerical analysis, and solutions of differential equations. q-Calculus is a generalization of many subjects, such as...
Springer, 2013 — 684 p.
Concrete Functional Calculus focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions. This includes composition of two functions, and the product integral, taking a matrix- or operator-valued coefficient function into a solution of a system of linear differential equations with the given coefficients. In this...
Учебник для вузов с углубленным изучением математики. — 5-е издание, стереотипное. — М.: Дрофа, Московский государственный университет имени М.В. Ломоносова (МГУ), 2004. — 384 с. — ISBN: 5-7107-8699-3. Учебник соответствует программе курсов «Функциональный анализ», «Теория операторов», «Анализ III», которые читаются в университетах и педагогических вузах. В книге приведены...
De Gruyter, 2011. — 233 р. — ISBN: 3110250306.
This textbook provides a self-contained and elementary introduction to the modern theory of pseudodifferential operators and their applications to partial differential equations. It presents the necessary material on Fourier transformation and distribution theory, the basic calculus of pseudodifferential operators on the...
McGraw-Hill, 1966. — 204 p.
Most texts on functional analysis (linear operator theory) deal almost exclusively with bounded, or continuous, operators. However, when one studies some problems on differential equations one needs to work with unbounded operators.
This book constitutes a good starting point to get acquainted with such operators, mostly with closed and strictly...
Кишинев: Штиинца, 1973. — 428 с.
Основное место в книге отведено теории линейных одномерных сингулярных интегральных операторов о непрерывными и разрывными коэффициентами в различных функциональных пространствах. При весьма общих ограничениях выясняются условия обратимости таких операторов, вид обратного оператора, структура ядра и коядра. Подробно рассматривается задача...
Pitman Books, 1982. - 379 pages. ISBN10: 0273085239 Foundations Metric and normed spaces Linear functionals and operators Elements of spectral theory Banach algebras Fredholm theory Compact operators in Hilbert space Integral operators in space of continuous functions Integration on manifolds Integral operators of compact manifolds Applications Integral operators in function...
Springer, 2003 - 548 p.
Together with "Theory of Operator Algebras I, II", this book, written by one of the most prominent researchers in the field of operator algebras, summarises the scientific work of the author focusing on von Neumann algebras and non-commutative integration. The book is part of the recently developed part of the "Encyclopaedia of Mathematical Sciences" on...
Springer, 2003 - 518 p.
Together with "Theory of Operator Algebras I, III", this book, written by one of the most prominent researchers in the field of operator algebras, summarises the scientific work of the author focusing on von Neumann algebras and non-commutative integration. The book is part of the recently developed part of the "Encyclopaedia of Mathematical Sciences" on...
Springer, 2001 - 415 p.
Since its inception by von Neumann 70 years ago, the theory of operator algebras has become a rapidly developing area of importance for the understanding of many areas of mathematics and theoretical physics. Accessible to the non-specialist, this first part of a three volume treatise provides a clear, carefully written survey that emphasizes the theory's...
Монографія. — Київ: НМК ВО, 1992. — 200 с. — ISBN: 5776314380. Дається виклад основ теорії додатних лінійних операторів типу В. Вивчаються апроксимаційні й асимптотичні властивості послідовностей цих операторів. На базі операторів типу В впроваджується клас багатовимірних розподілів, вивчаються їхні властивості, досліджуються статистичні оцінки праметрів. Для науковців,...
Springer, New York, 1983. — 285 p. The aim of this book is to give a simple and self-contained presentation of the theory of semigroups of bounded linear operators and its applications to partial differential equations. Generation and Representation: Uniformly Continuous Semigroups of Bounded Linear Operators Strongly Continuous Semigroups of Bounded Linear Operators The...
Institute of Mathematics of the Polish Academy of Sciences, 2007. - 155 pages. Linear spaces. Subspaces. Linear hull (span). Linear independence of elements. Dimension. Basis. Cartesian product. Direct sum. Complex extension of a real space. Quotient space. Codimension. Convex sets. Convex hulls. Linear manifolds. Hyperplanes. Algebras (linear rings). Ideals. Quotient algebras....
М.: МАИ, Современная математика. Фундаментальные направления. Том 9 (2004), 152 с.
Спектральная теория банаховых модулей
Абстрактные эргодические теоремы
Гармонический анализ в банаховых модулях над спектрально регулярными алгебрами
Оценки элементов обратных матриц и спектральный анализ линейных операторов
Спектральный анализ линейных отношений и вырожденные полугруппы...
Сборник. — Под ред. Г.П. Акилова. — Новосибирск: Наука, Сибирское отделение, 1977. — 339 с.: ил. — (АН СССР. Сибирское отделение. Институт математики). Сборник содержит обзоры ряда актуальных направлений современного функционального анализа. Особое внимание уделено геометрическим вопросам линейных топологических и упорядоченных векторных пространств, приложениям аналитических...
М.: Московский центр непрерывного математического образования (МЦНМО), 2010. — 176 c. — ISBN: 978-5-94057-573-3. Книга представляет собой записки семестрового курса лекций по спектральной теории, прочитанного автором в Независимом московском университете в весеннем семестре 2003 г. Ее можно рассматривать как дополнение к стандартному университетскому курсу функционального...
Монография. — К.: Выща школа, 1989. — 347 с. В монографии американского ученого рассмотрена теория полугрупп линейных операторов и ее приложения к дифференциальным уравнениям. Изучается важнейший класс полугрупп - сильно непрерывные полугруппы. С точки зрения полугрупп рассмотрены вопросы математической физики, теория рассеяния, движение несжимаемой жидкости, теория возмущений...
Монография. — Киев: Наукова думка, 1972. — 220 с. Монография посвящена построению спектральной теории обыкновенных дифференциальных операторов второго порядка с помощью операторов преобразования. Такой подход позволил единым способом и достаточно просто получить все основные результаты спектральной теории как в самосопряженном, так и в несамосопряженном случае. Особое внимание...
Birkhauser, 2006. - 204 pages. This book focuses on extremal problems. For instance, it seeks a domain which minimizes or maximizes a given eigenvalue of the Laplace operator with various boundary conditions and various geometric constraints. Also considered is the case of functions of eigenvalues. The text probes similar questions for other elliptic operators, such as...
2nd edition. — Springer-Verlag, 2001. — 288 p. This is the second edition of Shubin's classical book. It provides an introduction to the theory of pseudodifferential operators and Fourier integral operators from the very basics. The applications discussed include complex powers of elliptic operators, Hörmander asymptotics of the spectral function and eigenvalues, and methods of...
Монография. — М.: Наука, 2003. — 619 с.: ил. — ISBN 5-02-002865-7 (в пер.). В монографии представлены важнейшие результаты о мажорируемых операторах, полученные в последние двадцать лет и демонстрирующие сформировавшуюся теорию с широким кругом приложений. Изложение сосредоточено на строении мажорируемых операторов, подробно освещены вопросы разложения, продолжения и...
Учебное пособие. — Челябинск: Челябинский государственный университет (ЧелГУ), 1998. — 78 с. Настоящее пособие посвящено теории полугрупп и групп операторов с ядрами, разрешающих уравнения типа Соболева. Несмотря на научную новизну этой теории, материал изложен на уровне, доступном для студентов старших курсов математических специальностей. Приводится большое количество...
Учебное пособие. — Красноярск: Сибирский федеральный университет (СФУ), 2007. — 34 с. Методическая разработка для студентов физического факультета института естественных и гуманитарных наук. Линейные операторы и матрицы. Геометрические примеры линейных операторов. Арифметические примеры линейных операторов. Алгебраические примеры линейных операторов. Замена базиса....
Перевод с английского А. И. Комета и М. А. Шубина. — Под редакцией М. А. Шубина. — М.: Мир, 1984. — 400 с. Второй том двухтомной монографии, посвященной систематическому изложению микролокального анализа — основного современного средства исследования разнообразных задач для уравнений в частных производных. Значительная часть материала в монографическом виде представлена...
American Mathematical Society, 1996. - 283 pages. The objectives of this monograph are to present some topics from the theory of monotone operators and nonlinear semigroup theory which are directly applicable to the existence and uniqueness theory of initial-boundary-value problems for partial differential equations and to construct such operators as realizations of those...
Imperial College Press, 2010. - 200 pages. Over the last decade, there has been considerable interest and progress in determining the spectral properties of various operators that take relativistic effects into account, with important implications for mathematics and physics. Difficulties are encountered in many-particle problems due to the lack of semiboundedness of the Dirac...
Издание второе, переработанное и дополненное. — М.: Наука, 1969. — 528 с. Книга посвящена основам теории обыкновенных линейных дифференциальных операторов и некоторым ее приложениям. Она состоит из двух частей. В более элементарной первой части изложены: основные понятия и основные задачи теории дифференциальных операторов, асимптотическое поведение собственных значений и...
М.: Наука, Главная редакция физико-математической литературы, 1980. — 383 с. В книге излагается спектральная теория на функциональной модели Секефальви-Надя — Фойаша в сравнительно простом ее варианте (одномерный ранг неунитарности). Подробно разработаны все тонкости теории вплоть до обобщенных спектральных разложений. Прослежены очень тесные и плодотворные связи с теорией...
Монография. — М.: Физматлит, 1993. — 464 с. — ISBN 5020142670. Изложены основные вопросы теории усреднения и G-сходимости эллиптических и параболических операторов любого порядка, а также нелинейных эллиптических операторов вариационного типа. Приводятся с доказательствами некоторые необходимые сведения из теории краевых задач, гармонического анализа, эргодической теории....
Монография. — М.: Государственное издательство физико-математической литературы, 1963. — 339 с. Монография посвящена изложению основ и развитию применений прямых методов исследования природы спектра сингулярных дифференциальных операторов. В ней отражена соответствующая журнальная литература за последние 10—15 лет. Среди рассматриваемых операторов центральное место занимает...
Монография. — Кишинев: Штиинца, 1986. — 260 с. Ответственный редактор кандидат физико-математических наук Г.И. Руссу. Монография содержит изложение основ спектральной теории полиномиальных операторных пучков в гильбертовом пространстве. Основное внимание уделяется фундаментальным результатам М. В. Келдыша о кратной полноте собственных и присоединенных векторов пучка и об...
Монография. — Харьков: Харьковский государственный университет, 1971. — 160 с. Операторный узел — новое математическое понятие, возникшее в теории несамосопряженных и неунитарных Операторов как необходимое обобщение линейного оператора. В монографии развивается исчисление операторных узлов и соответствующих им открытых систем. Значительная часть ее посвящена теории...
Монография. — Перев. с англ. Г.М. Жнелина. — С дополнением М.А. Антонца, Г.М. Жислина и И.А. Шерешевского. — М.: Мир, 1976. — 152 с. Единственная в мировой литературе монография, посвященная строгому качественному исследованию гамильтоновых операторов. Написана на основе оригинальных работ авторов. Ими получено описание спектра для широкого класса операторов при весьма слабых...
Монография. — Перевод с английского А.И. Комета и М.А. Шубина. — Под редакцией М.А. Шубина. — М.: Мир, 1984. — 400 с. Первый том двухтомной монографии посвященный систематическому изложению микролокального анализа.
Macmillan, 1953. - 466 pages. THE consideration of linear operators follows in a natural way from a study of infinite matrices, which form an important particular case when the matrices are associative. This book is, however, complete in itself, in that it is not essential to know more than the most elementary properties of infinite matrices; where such knowledge is required,...
Учебник. — М.: Физматгиз, 1959. — 213 с. Книга является учебником по конструктивной теории функций, рассчитанным на лиц, владеющих математическим анализом. в объеме программы физико-математических факультетов педагогических институтов. Линейные положительные функционалы и операторы. Линейные положительные функционалы. Линейные положительные операторы. Приближение функций...
Myers Press, 2008. - 648 Pages. Originally published in 1936. Contents include: Chapter I Linear operators. Chapter II Particular operators. Chapter III The theory of linear system of equations. Chapter IV Operational multiplication and inversion. Chapter V Grades definited by special operators. Chapter VI Differential equations of infinite order with constant coefficients. In...
Учебное пособие. — Л.: Ленинградский государственный университет имени А.А. Жданова (ЛГУ), 1980. — 264 с. В учебном пособии изложен основной материал по спектральной теории операторов. Большое место отведено специальным разделан теории операторов, важным для приложений в математической и теоретической физике (теория возмущений, спектральная теория дифференциальных операторов,...
Киев: Наукова думка, 1965. — 779 с. В книге излагается теория разложений по собственным функциям самосопряженных операторов. Общая теория прилагается к построению подобных разложений для дифференциальных операторов в частных производных и разностных операторов, к получению интегральных представлений положительно определенных ядер, к проблеме моментов и т. д. Наряду с построением...
Москва: Московский государственный институт электроники и математики (МИЭМ), 2004. — 80 с. Лекции 1-14 (второй семестр) по исчислению псевдодифференциальных операторов в n-мерных пространствах. МИЭМ, факультет прикладной математики.
Москва: Московский государственный институт электроники и математики (МИЭМ), 2003. — 53 с. Лекции 1-11 (первый семестр) по исчислению псевдодифференциальных операторов в n-мерных пространствах. МИЭМ, факультет прикладной математики.
Учебное пособие. — Тамбов: Тамбовский государственный технический университет (ТГТУ), 2009. — 32 с. Изложены начальные положения теории линейных операторов, предписанные к изучению действующим образовательным стандартом в области естественно-математических дисциплин. Рекомендуются к использованию студентами 2 курса инженерно-технических специальностей дневной формы обучения.
Киев: Наукова думка, 1978. В книге рассматривается некоторый математический аппарат, полезный при изучении самосопряженных операторов, действующих в пространствах функций бесконечного числа переменных. Точнее, идет речь об операторах, действующих в бесконечных тензорных произведениях пространств, изоморфных образах таких произведений, или их пополнений по некоторым...
Монография. — Перев. с англ. Г.А. Воропаевой, А.М. Стёпиной, И.А. Шишмарёвой. — Под ред. В.П. Маслова. — М.: Мир, 1972. — 740 с. Монография крупнейшего японского математика Т. Като представляет собой выдающееся явление в математической литературе. Она посвящена важному разделу функционального анализа, тесно связанному с современной теоретической физикой. Книга написана с...
М.: Наука, 1991. — 368 c. Посвящена в основном проблемам сходимости и суммируемости спектральных разложений по фундаментальным функциям самосопряженных эллиптических операторов второго порядка. Для произвольных самосопряяженных неотрицательных расширений таких операторов и их средних Рисса установлены условия равномерной сходимости, окончательные в каждом из классов функций...
Монография. — Москва: Наука, Главная редакция физико-математической литературы издательства, 1978. — 400 с. Книга посвящена одному из важных направлений функционального анализа - теории интерполяции линейных операторов. Излагаются основные методы построения интерполяционных пространств, изучаются их свойства. Эти методы позволяют с новых позиций взглянуть на ряд тем и...
Монография. — Перев. с англ. Р.С. Исмагилова и Б.С. Митягина. — Под ред. А.Г. Костюченко. — М.: Мир, 1974. — 662 с. Эта книга - заключительный том хорошо известной фундаментальной монографии по теории операторов. Он посвящен спектральным операторам - важному классу несамосопряженных операторов. В нем систематически излагается теория этих операторов, рассматривается вопрос об их...
Монография. — Перев. с англ. Р.С. Исмагилова и Б.С. Митягина. — Под ред. А.Г. Костюченко. — М.: Мир, 1966. — 1064 с. Эта книга представляет собой второй том фундаментальной монографии по теории линейных операторов (первый том был выпущен Издательством иностранной литературы в 1962 г. ); она посвящена многочисленным применениям теории линейных операторов к различным вопросам...
Монография. — Перев. с англ. Р.С. Исмагилова и Б.С. Митягина. — Под ред. А.Г. Костюченко. — М.: Издательство иностранной литературы, 1962. — 896 с. Первый том фундаментальной монографии по теории линейных операторов. Книга содержит подготовительный материал: теоретико-множественные, топологические и алгебраические понятия, основные принципы линейного анализа, теорию...
М.: Наука, Главная редакция физико-математической литературы, 1965. — 448 с.
Теория несамосопряженных операторов необходима для математического изучения процессов, которые возникают в неконсервативных системах, играющих большую роль в современной физике и механике. В книге впервые дается развернутое описание ряда методов теории несамосопряженных операторов в гильбертовом...
Учебник. — 2-e издание. — М.: Московский государственный университет имени М.В. Ломоносова (МГУ), 1986. — 368 с. Учебник соответствует программе курсов «Функциональный анализ», «Теория операторов», «Анализ III», которые читаются в университетах и педагогических вузах. В книге приведены основные теоретико-множественные понятия, представлена общая теория метрических,...
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