Harmonic analysis on symmetric spaces -- Euclidean space, the sphere, and the Poincaré upper half-plane / Audrey Terras
| データ種別 | 電子書籍 |
|---|---|
| 版 | Second edition. |
| 出版者 | New York : Springer |
| 出版年 | [2013] |
書誌詳細を非表示
| 書誌ID | OB01025205 |
|---|---|
| 本文言語 | 英語 |
| 一般注記 | Includes bibliographical references and index 1. Flat space: Fourier analysis on Rm -- 2. A compact symmetric space: the sphere -- 3. The Poincaré upper half-plane. License restrictions may limit access Summary: This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincaré upper half plane. This book is intended for beginning graduate students in mathematics or researchers in physics or engineering. Written with an informal style, the book places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, and engineering. Many corrections, new topics, and updates have been incorporated in this new edition. These include discussions of the work of P. Sarnak and others making progress on various conjectures on modular forms, the work of T. Sunada, Marie-France Vignras, Carolyn Gordon, and others on Mark Kac's question "Can you hear the shape of a drum?", Ramanujan graphs, wavelets, quasicrystals, modular knots, triangle and quaternion groups, computations of Maass waveforms, and, finally, the author's comparisons of continuous theory with the finite analogues. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, Poisson's summation formula and applications in crystallography and number theory, applications of spherical harmonic analysis to the hydrogen atom, the Radon transform, non-Euclidean geometry on the Poincaré upper half plane H or unit disc and applications to microwave engineering, fundamental domains in H for discrete groups, tessellations of H from such discrete group actions, automorphic forms, the Selberg trace formula and its applications in spectral theory as well as number theory.-- Source other than Library of Congress |
| 著者標目 | *Terras, Audrey |
| 件 名 | LCSH:Harmonic analysis LCSH:Fourier analysis LCSH:Symmetric spaces |
| 分 類 | LCC:QA403 DC23:515/.2433 |
| 巻冊次 | alk. paper ; ISBN:9781461479710 RefWorks出力（各巻） alk. paper ; ISBN:1461479711 RefWorks出力（各巻） ebk. ; ISBN:9781461479727 RefWorks出力（各巻） |
| 資料種別 | 機械可読データファイル |
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