Type(s) de contenu et mode(s) de consultation : Texte noté : électronique

Auteur(s) : Terras, Audrey  Voir les notices liées en tant qu'auteur

Titre(s) : Harmonic analysis on symmetric spaces -- Euclidean space, the sphere, and the Poincaré upper half-plane [Texte électronique] / Audrey Terras

Édition : 2nd edition

Publication : New York : Springer, cop. 2013

Description matérielle : 1 ressource dématérialisée

Note(s) : Includes bibliographical references (pages 377-401) and index
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

Sujet(s) : Analyse harmonique (mathématiques)  Voir les notices liées en tant que sujet
Fourier, Analyse de  Voir les notices liées en tant que sujet
Espaces symétriques hermitiens  Voir les notices liées en tant que sujet

Indice(s) Dewey :  515.243 3 (23e éd.) = Analyse de Fourier et analyse harmonique  Voir les notices liées en tant que sujet

Identifiants, prix et caractéristiques : ISBN 9781461479727

Identifiant de la notice  : ark:/12148/cb446660838

Notice n° :  FRBNF44666083 (notice reprise d'un réservoir extérieur)

Table des matières : 1. Flat space: Fourier analysis on Rm ; 2. A compact symmetric space: the sphere ; 3. The Poincaré upper half-plane.