Harmonic Analysis on Symmetric Spaces<U+0014>Euclidean Space, the Sphere, and the Poincar ̌Upper Half-Plane

• Main Author: Terras, Audrey. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2013.
• Edition: 2nd ed. 2013.
• Subjects: Mathematics.; Group theory.; Topological Groups.; Harmonic analysis.; Fourier analysis.; Functions of complex variables.; Functions, special.; Abstract Harmonic Analysis.; Fourier Analysis.; Group Theory and Generalizations.; Topological Groups, Lie Groups.; Functions of a Complex Variable.; Special Functions.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-1-4614-7972-7

This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincar ̌upper half plane. This book is intended for beginning graduate students in mathematics or researchers in physics or engineering. Written with an informal st...

Table of Contents:

• Chapter 1 Flat Space. Fourier Analysis on R^m.
• 1.1 Distributions or Generalized Functions
• 1.2 Fourier Integrals
• 1.3 Fourier Series and the Poisson Summation Formula
• 1.4 Mellin Transforms, Epstein and Dedekind Zeta Functions
• 1.5 Finite Symmetric Spaces, Wavelets, Quasicrystals, Weyl<U+0019>s Criterion for Uniform Distribution
• Chapter 2 A Compact Symmetric Space
• The Sphere
• 2.1 Fourier Analysis on the Sphere
• 2.2 O(3) and R^3. The Radon Transform
• Chapter 3 The Poincar ̌Upper Half-Plane
• 3.1 Hyperbolic Geometry
• 3.2 Harmonic Analysis on H
• 3.3 Fundamental Domains for Discrete Subgroups <U+0093> of G = SL(2, R)
• 3.4 Modular of Automorphic Forms
• Classical
• 3.5 Automorphic Forms
• Not So Classical
• Maass Waveforms
• 3.6 Modular Forms and Dirichlet Series. Hecke Theory and Generalizations
• References
• Index.