عنوان

Harmonic analysis on symmetric spaces--Euclidean space, the sphere, and the Poincaré upper half-plane /

(Number (ISBN

146147972X (electronic bk.)

(Number (ISBN

9781461479727 (electronic bk.)

Erroneous ISBN

9781461479710

Number

dltt

Title Proper

Harmonic analysis on symmetric spaces--Euclidean space, the sphere, and the Poincaré upper half-plane /

General Material Designation

[Book]

First Statement of Responsibility

Audrey Terras

Edition Statement

Second edition

Specific Material Designation and Extent of Item

1 online resource (xvii, 413 pages) :

Other Physical Details

illustrations

Text of Note

Includes bibliographical references and index

Text of Note

Chapter 1. Flat Space. Fourier Analysis on R̂m. -- Chapter 2. A Compact Symmetric Space--The Sphere -- Chapter 3. The Poincaré Upper Half-Plane

0

Text of Note

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

Title

OhioLINK electronic book center (Online)

Title

SpringerLink

Fourier analysis

Harmonic analysis

MAT034000

PBKD

Number

Edition

Class number

Class number

Terras, Audrey

Ohio Library and Information Network

Date of Transaction

20131202122227.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y