Description: Harmonic Analysis on Symmetric Spacesùeuclidean Space, the Sphere, and the Poincar? Upper Half-plane : Euclidean Space, the Sphere, and the Poincare Upper Half-Plane, Hardcover by Terras, Audrey, ISBN 1461479711, ISBN-13 9781461479710, Like New Used, Free shipping in the US 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, th places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, and engineering. Many corrections and updates have been incorporated in this new edition. Updates include discussions of P. Sarnak and others' work on quantum chaos, the work of T. Sunada, Marie-France Vignéras, Carolyn Gordon, and others on Mark Kac's question "Can you hear the shape of a drum?", A. Lubotzky, R. Phillips and P. Sarnak's examples of Ramanujan graphs, 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 G, tessellations of H from such discrete group actions, automorphic forms, and the Selberg trace formula and its applications in spectral theory as well as number theory.
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Book Title: Harmonic Analysis on Symmetric Spacesùeuclidean Space, the Sphere
Number of Pages: Xvii, 413 Pages
Language: English
Publication Name: Harmonic Analysis on Symmetric Spaces--Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane
Publisher: Springer New York
Subject: Group Theory, Algebra / Abstract, Mathematical Analysis
Publication Year: 2013
Item Weight: 271.1 Oz
Type: Textbook
Subject Area: Mathematics
Item Length: 9.3 in
Author: Audrey Terras
Item Width: 6.1 in
Format: Hardcover
