Harmonic Function Theory
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ISBN-13:
9780387952185
Veröffentl:
2001
Erscheinungsdatum:
25.01.2001
Seiten:
264
Autor:
Sheldon Axler
Gewicht:
515 g
Format:
244x162x22 mm
Sprache:
Englisch
Beschreibung:
This 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.
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 new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bocher's Theorem, new exercises and proofs, aa 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.
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