Haslinger F. The d-bar Neumann Problem and Schrödinger Operators

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, updates to Schrödinger operators with magnetic fields and new results in the field of compactness.
Explores the Segal Bargmann Space (Fock space) connection to quantum mechanics.
Updates to Schrödinger operators with magnetic fields
New results about compactness, in particular a necessary condition of compactness 　Preface to the first edition
Preface to the second edition
Bergman spaces
The canonical solution operator to ᾱ
Spectral properties of the canonical solution operator to ᾱ
The ᾱ-complex
Density of smooth forms
The weighted ᾱ-complex
The twisted ᾱ-complex
Applications
Spectral analysis
Schrödinger operators and Witten Laplacians
Compactness
The ᾱ-Neumann operator and the Bergman projection
Compact resolvents
Spectrum of ◻ on the Fock space
Obstructions to compactness
The ᾱ-complex on the Segal–Bargmann space
Bibliography
Index