Harmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Algebra
Cover of the book Harmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane by Audrey Terras, Springer New York
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Audrey Terras ISBN: 9781461479727
Publisher: Springer New York Publication: September 12, 2013
Imprint: Springer Language: English
Author: Audrey Terras
ISBN: 9781461479727
Publisher: Springer New York
Publication: September 12, 2013
Imprint: Springer
Language: English

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 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 Γ, 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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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 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 Γ, 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.

More books from Springer New York

Cover of the book Extra Dimensions in Space and Time by Audrey Terras
Cover of the book Exercise and Cancer Survivorship by Audrey Terras
Cover of the book Food Safety Management by Audrey Terras
Cover of the book Evolution That Anyone Can Understand by Audrey Terras
Cover of the book Scientific Ballooning by Audrey Terras
Cover of the book The Next Economics by Audrey Terras
Cover of the book Imaging Coronary Atherosclerosis by Audrey Terras
Cover of the book GHRH, GH, and IGF-I by Audrey Terras
Cover of the book Distributed Hash Table by Audrey Terras
Cover of the book Nuclear Medicine Technology Study Guide by Audrey Terras
Cover of the book Graphene Nanoelectronics by Audrey Terras
Cover of the book United States Health Care Policymaking by Audrey Terras
Cover of the book Molecular mechanisms and physiology of disease by Audrey Terras
Cover of the book Structured Peer-to-Peer Systems by Audrey Terras
Cover of the book Nitroazoles: Synthesis, Structure and Applications by Audrey Terras
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy