Harmonic Analysis on Symmetric Spaces-Higher Rank Spaces, Positive Definite Matrix Space and Generalizations...

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Audrey Terras

Harmonic Analysis on Symmetric Spaces-Higher Rank Spaces, Positive Definite Matrix Space and Generalizations

Audrey Terras

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English

Springer-Verlag New York Inc.
21 April 2018

Number theory; Complex analysis, complex variables; Geometry; Combinatorics & graph theory; Applied mathematics

This text is an introduction to harmonic analysis on symmetric spaces, focusing on advanced topics such as higher rank spaces, positive definite matrix space and generalizations. It is intended for beginning graduate students in mathematics or researchers in physics or engineering. As with the introductory book entitled Harmonic Analysis on Symmetric Spaces - Euclidean Space, the Sphere, and the Poincare Upper Half Plane, the style is informal with an emphasis on motivation, concrete examples, history, and applications. The symmetric spaces considered here are quotients X=G/K, where G is a non-compact real Lie group, such as the general linear group GL(n,P) of all n x n non-singular real matrices, and K=O(n), the maximal compact subgroup of orthogonal matrices. Other examples are Siegel's upper half plane and the quaternionic upper half plane . In the case of the general linear group, one can identify X with the space Pn of n x n positive definite symmetric matrices.

Many corrections and updates have been incorporated in this new edition. Updates include discussions of random matrix theory and quantum chaos, as well as recent research on modular forms and their corresponding L-functions in higher rank. Many applications have been added, such as the solution of the heat equation on Pn, the central limit theorem of Donald St.

P. Richards for Pn, results on densest lattice packing of spheres in Euclidean space, and GL(n)-analogs of the Weyl law for eigenvalues of the Laplacian in plane domains.

Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, fundamental domains in X for discrete groups (such as the modular group GL(n,Z) of n x n matrices with integer entries and determinant +/-1), connections with the problem of finding densest lattice packings of spheres in Euclidean space, automorphic forms, Hecke operators, L-functions, and the Selberg trace formula and its applications in spectral theory as well as number theory.

By: Audrey Terras
Imprint: Springer-Verlag New York Inc.
Country of Publication: United States
Edition: Softcover reprint of the original 2nd ed. 2016
Dimensions: Height: 235mm, Width: 155mm, Spine: 26mm
Weight: 7.548kg
ISBN: 9781493980420
ISBN 10: 1493980424
Pages: 487
Publication Date: 21 April 2018
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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

Reviews for Harmonic Analysis on Symmetric Spaces-Higher Rank Spaces, Positive Definite Matrix Space and Generalizations

Advanced graduate students and beginners in harmonic analysis on symmetric spaces are surely motivated and attracted by abundant examples, relevant history, and exercises. Excellent references in each section are useful for experts. (Takeshi Kawazoe, Mathematical Reviews, August, 2017) It is very nice to have available, now, the second, updated version of the entire set ... . Audrey Terras has done the mathematical community (and not just number theorists and modular formers) a great service: these books are a major contribution on several fronts, including the pedagogical one. They are of course also excellent references for various mathematical themes that are otherwise scattered all through the recent literature. (Michael Berg, MAA Reviews, maa.org, July, 2016) It is very nice to have available, now, the second, updated version of the entire set ... . Audrey Terras has done the mathematical community (and not just number theorists and modular formers) a great service: these books are a major contribution on several fronts, including the pedagogical one. They are of course also excellent references for various mathematical themes that are otherwise scattered all through the recent literature. (Michael Berg, MAA Reviews, maa.org, July, 2016) It is very nice to have available, now, the second, updated version of the entire set . Audrey Terras has done the mathematical community (and not just number theorists and modular formers) a great service: these books are a major contribution on several fronts, including the pedagogical one. They are of course also excellent references for various mathematical themes that are otherwise scattered all through the recent literature. (Michael Berg, MAA Reviews, maa.org, July, 2016)