登入選單
返回Google圖書搜尋
Harmonic Function Theory
Sheldon AxlerPaul BourdonRamey Wade
出版Springer Science & Business Media, 2001-01-25
主題Mathematics / CalculusMathematics / Differential Equations / GeneralMathematics / Differential Equations / PartialMathematics / Probability & Statistics / Stochastic ProcessesMathematics / Vector AnalysisMathematics / Mathematical AnalysisMedical / General
ISBN03879521879780387952185
URLhttp://books.google.com.hk/books?id=wATLzBfup-wC&hl=&source=gbs_api
EBookSAMPLE
註釋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.