| 书目名称 | Principles of Harmonic Analysis |
| 编辑 | Anton Deitmar,Siegfried Echterhoff |
| 视频video | |
| 概述 | Contains material unavailable elsewhere, including the full proof of Pontryagin Duality and the Plancherel Theorem.Authors emphasize Banach algebras as the cleanest way to get many fundamental results |
| 丛书名称 | Universitext |
| 图书封面 |  |
| 描述 | The tread of this book is formed by two fundamental principles of Harmonic Analysis: the Plancherel Formula and the Poisson S- mation Formula. We ?rst prove both for locally compact abelian groups. For non-abelian groups we discuss the Plancherel Theorem in the general situation for Type I groups. The generalization of the Poisson Summation Formula to non-abelian groups is the S- berg Trace Formula, which we prove for arbitrary groups admitting uniform lattices. As examples for the application of the Trace F- mula we treat the Heisenberg group and the group SL (R). In the 2 2 former case the trace formula yields a decomposition of the L -space of the Heisenberg group modulo a lattice. In the case SL (R), the 2 trace formula is used to derive results like the Weil asymptotic law for hyperbolic surfaces and to provide the analytic continuation of the Selberg zeta function. We ?nally include a chapter on the app- cations of abstract Harmonic Analysis on the theory of wavelets. The present book is a text book for a graduate course on abstract harmonic analysis and its applications. The book can be used as a follow up of the First Course in Harmonic Analysis, [9], or indep- dently, if t |
| 出版日期 | Textbook 2009 |
| 关键词 | Abelian group; Fourier series; Hilbert space; algebra; boundary element method; duality; form; function; fun |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-0-387-85469-4 |
| isbn_softcover | 978-0-387-85468-7 |
| isbn_ebook | 978-0-387-85469-4Series ISSN 0172-5939 Series E-ISSN 2191-6675 |
| issn_series | 0172-5939 |
| copyright | Springer-Verlag New York 2009 |
发表于 2025-3-21 18:31:56
