検索結果をRefWorksへエクスポートします。対象は1件です。
Export
RT Book, Whole SR Electronic DC OPAC T1 Harmonic analysis on symmetric spaces -- Euclidean space, the sphere, and the Poincaré upper half-plane A1 Terras, Audrey YR 2013 FD [2013] VO alk. paper K1 Harmonic analysis K1 Fourier analysis K1 Symmetric spaces ED Second edition. PB Springer PP New York SN 9781461479710 LA English (英語) CL LCC:QA403 CL DC23:515/.2433 NO Includes bibliographical references and index NO 1. Flat space: Fourier analysis on Rm -- 2. A compact symmetric space: the sphere -- 3. The Poincaré upper half-plane. NO License restrictions may limit access NO 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 NO 書誌ID=OB01025205; LK https://link.springer.com/openurl?genre=book&isbn=978-1-4614-7972-7 DS 同志社大学OPAC OL 30