Harmonic function theory. 2nd ed

種類:

電子ブック

責任表示:

Sheldon Axler, Paul Bourdon, Wade Ramey

出版情報:

New York : Springer, 2001

著者名:

• Axler, Sheldon Jay.
• Bourdon, Paul.
• Ramey, Wade.

シリーズ名:

Graduate texts in mathematics ; ; 137

ISBN:

9780387215273 [0387215271]    
9781475781373 [1475781377]    
9781441929112 [1441929118]    
9786610189700 [6610189706]    

注記:

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 d
English
Includes bibliographical references (pages 249-250) and indexes
Print version record

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