| 书目名称 | Harmonic Function Theory |
| 编辑 | Sheldon Axler,Paul Bourdon,Wade Ramey |
| 视频video | |
| 丛书名称 | Graduate Texts in Mathematics |
| 图书封面 |  |
| 描述 | 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. |
| 出版日期 | Textbook 19921st edition |
| 关键词 | Harmonic Function Theory; Harmonic Functions; Laplace‘s equation; complex analysis; functional analysis; |
| 版次 | 1 |
| doi | https://doi.org/10.1007/b97238 |
| isbn_ebook | 978-0-387-21527-3Series ISSN 0072-5285 Series E-ISSN 2197-5612 |
| issn_series | 0072-5285 |
| copyright | Springer Science+Business Media New York 1992 |
发表于 2025-3-21 17:43:44
