Axler S., Bourdon P., Ramey W. Harmonic Function Theory

Springer, 2001. — 270 p. — 2nd ed. — ISBN: 0387952187, 9780387952185This book is about harmonic functions in Euclidean space. This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package supplements the text for readers who wish to explore harmonic function theory on a computer.Basic Properties of Harmonic Functions
Bounded Harmonic Functions
Positive Harmonic Functions
The Kelvin Transform
Harmonic Polynomials
Harmonic Hardy Spaces
Harmonic Functions on Half-Spaces
Harmonic Bergman Spaces
The Decomposition Theorem
Annular Regions
The Dirichlet Problem and Boundary Behavior
Volume, Surface Area, and Integration on Spheres
Harmonic Function Theory and MathematicaSymbol Index