Harmonic function theory /
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, emphasiz...
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| Other Authors: | , |
| Format: | eBook |
| Language: | English |
| Published: |
New York :
Springer,
2001.
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| Edition: | 2nd ed. |
| Series: | Graduate texts in mathematics ;
137. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book Connect to the full text of this electronic book |
| Summary: | 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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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (xi, 259 pages) : illustrations. |
| Bibliography: | Includes bibliographical references (pages 249-250) and indexes. |
| ISBN: | 0387215271 (electronic bk.) 9780387215273 (electronic bk.) 9781475781373 (electronic bk.) 1475781377 (electronic bk.) |