調和解析理論（第２版） Harmonic Function Theory (Graduate Texts in Mathematics Vol.137)

Axler, Sheldon/ Bourdon, Paul/ Ramey, Wade

Springer（2001発売）

• 製本 Hardcover:ハードカバー版／ページ数 280 p.
• 商品コード 9780387952185

基本説明

A book about harmonic functions in Euclidean space. The authors have taken unusual care to motivate concepts and simplify proofs.

Full Description

This is a book about harmonic functions in Euclidean space. Readers with a background in real and complex analysis at the beginning graduate level will feel comfortable with the material presented here. The authors have taken unusual care to motivate concepts and simplify proofs. Topics include: basic properties of harmonic functions, Poisson integrals, the Kelvin transform, spherical harmonics, harmonic Hardy spaces, harmonic Bergman spaces, the decomposition theorem, Laurent expansions, isolated singularities, and the Dirichlet problem. The new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bocher's Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package-designed by the authors and available by e-mail - supplements the text for readers who wish to explore harmonic function theory on a computer.

Contents

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.