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Synopsis
Harmonic functions - the solutions of Laplace's equation - play a crucial role in many areas of mathematics, physics, and engineering. Avoiding the disorganization and inconsistent notation of other expositions, the authors approach the field from a more function-theoretic perspective, emphasizing techniques and results that will seem natural to mathematicians comfortable with complex function theory and harmonic analysis; prerequisites for the book are a solid foundation in real and complex analysis together with some basic results from functional analysis. Topics covered include: basic properties of harmonic functions defined on subsets of Rn, including Poisson integrals; properties bounded functions and positive functions, including Liouville's and Cauchy's theorems; the Kelvin transform; Spherical harmonics; hp theory on the unit ball and on half-spaces; harmonic Bergman spaces; the decomposition theorem; Laurent expansions and classification of isolated singularities; and boundary behavior. An appendix describes routines for use with MATHEMATICA to manipulate some of the expressions that arise in the study of harmonic functions.
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Review
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)
"About this title" may belong to another edition of this title.
- PublisherSpringer-Verlag
- Publication date1992
- ISBN 10 0387978755
- ISBN 13 9780387978758
- BindingHardcover
- LanguageEnglish
- Edition number1
- Number of pages231
- IllustratorB7W Equations
- Rating
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Harmonic Function Theory (Graduate Texts in Mathematics, Vol 137)
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Springer-Verlag (edition F First Edition), 1992
ISBN 10: 0387978755
ISBN 13: 9780387978758
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Harmonic Function Theory (Graduate Texts in Mathematics, Vol 137)
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Harmonic Function Theory (Graduate Texts in Mathematics, Vol 137)
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