Groups and Geometric Analysis: Integral Geometry, Invariant Differential Operators, and Spherical Functions
About this Title
Sigurdur Helgason, Massachusetts Institute of Technology, Cambridge, MA
Publication: Mathematical Surveys and Monographs
Publication Year 1984: Volume 83
ISBNs: 978-0-8218-2673-7 (print); 978-1-4704-1310-1 (online)
MathSciNet review: MR1790156
MSC: Primary 22-02; Secondary 22E30, 22E46, 43A85, 43A90, 44A12, 53-02, 58-02
Group-theoretic methods have taken an increasingly prominent role in analysis. Some of this change has been due to the writings of Sigurdur Helgason. This book is an introduction to such methods on spaces with symmetry given by the action of a Lie group. The introductory chapter is a self-contained account of the analysis on surfaces of constant curvature. Later chapters cover general cases of the Radon transform, spherical functions, invariant operators, compact symmetric spaces and other topics. This book, together with its companion volume, Geometric Analysis on Symmetric Spaces (AMS Mathematical Surveys and Monographs series, vol. 39, 1994), has become the standard text for this approach to geometric analysis.
Sigurdur Helgason was awarded the Steele Prize for outstanding mathematical exposition for Groups and Geometric Analysis and Differential Geometry, Lie Groups and Symmetric Spaces.
Graduate students and research mathematicians interested in analysis on homogeneous spaces, differential geometry, and topological groups, Lie groups.
Table of Contents
- Introduction: Geometric Fourier analysis on spaces of constant curvature
- I. Integral geometry and Radon transforms
- II. Invariant differential operators
- III. Invariants and harmonic polynomials
- IV. Spherical functions and spherical transforms
- V. Analysis on compact symmetric spaces