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.
Reviews / Votes
From the reviews of the second edition:
"There are several major changes in this second edition . . Many exercises have been added and several photographs of mathematicians related to harmonic functions are included. The book is a nice introduction to the fundamental notions of potential theory." (European Mathematical Society Newsletter, June, 2002)
"We warmly recommend this textbook to graduate students interested in Harmonic Function Theory and/or related areas. We are sure that the reader will be able to appreciate the lively and illuminating discussions in this book, and therefore, will certainly gain a better understanding of the subject." (Ferenc Móricz, Acta Scientiarum Mathematicarum, Vol. 67, 2001)
"This is a new edition of a nice textbook . on harmonic functions in Euclidean spaces, suitable for a beginning graduate level course. . New exercises are added and numerous minor improvements throughout the text are made." (Alexander Yu. Rashkovsky, Zentralblatt MATH, Vol. 959, 2001)
Series
Edition
Language
Place of publication
Target group
Primary & secondary/elementary & high school
Graduate
Edition type
Product notice
sewn/stitched
Cloth over boards
Illustrations
Dimensions
Height: 244 mm
Width: 162 mm
Thickness: 22 mm
Weight
ISBN-13
978-0-387-95218-5 (9780387952185)
DOI
10.1007/978-1-4757-8137-3
Schweitzer Classification
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.
