Harmonic Analysis on Symmetric Spaces―Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane: Euclidean Space, the Sphere, and the Poincare Upper Half-Plane - Hardcover

Terras, Audrey

Hardcover

ISBN 10: 1461479711 ISBN 13: 9781461479710

Publisher: Springer, 2013

Synopsis

This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincare 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 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 Vigneras, 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 Poincare 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, and the Selberg trace formula and its applications in spectral theory as well as number theory.

About this title

Review

From the reviews of the second edition:

An updated version of an established work of scholarship that has both stood the test of time, and remains very relevant and well-worth reading. The intended audience is very broad, and includes scientists outside of pure mathematics ... as well as mathematicians who wish to enter the indicated field and desire a very well-drawn road-map. ... And doing the exercises is a solid pedagogical experience that will inaugurate the novice as well as the interested visitor into active areas of research. --(Michael Berg, MAA Reviews, November, 2013)

About the Author

Audrey Anne Terras is currently Professor Emerita of Mathematics at the University of California at San Diego.

Edition details

• Publisher: Springer
• Publication date: 2013
• ISBN 10: 1461479711
• ISBN 13: 9781461479710
• Binding: Hardcover
• Language: English
• Edition number: 2
• Number of pages: 430