Analysis on Lie Groups: An Introduction

by Jacques Faraut

Overview

This self-contained text concentrates on the perspective of analysis, assuming only elementary knowledge of linear algebra and basic differential calculus. The author describes, in detail, many interesting examples, including formulas which have not previously appeared in book form. Topics covered include the Haar measure and invariant integration, spherical harmonics, Fourier analysis and the heat equation, Poisson kernel, the Laplace equation and harmonic functions. Perfect for advanced undergraduates and graduates in geometric analysis, harmonic analysis and representation theory, the tools developed will also be useful for specialists in stochastic calculation and the statisticians. With numerous exercises and worked examples, the text is ideal for a graduate course on analysis on Lie groups.

Product Details

ISBN-13:	9780521719308
Publisher:	Cambridge University Press
Publication date:	05/22/2008
Series:	Cambridge Studies in Advanced Mathematics , #110
Pages:	314
Product dimensions:	6.10(w) x 9.00(h) x 0.80(d)

About the Author

Jacques Faraut is Professeur Émérite in the Institut de Mathématiques de Jussieu at the Université Pierre et Marie Curie in Paris.

Table of Contents

Preface; 1. The linear group; 2. The exponential map; 3. Linear Lie groups; 4. Lie algebras; 5. Haar measure; 6. Representations of compact groups; 7. The groups SU(2) and SO(3), Haar measure; 8. Analysis on the group SU(2); 9. Analysis on the sphere; 10. Analysis on the spaces of symmetric and Hermitian matrices; 11. Irreducible representations of the unitary group; 12. Analysis on the unitary group; Bibliography; Index.

Editorial Reviews

"The main themes are carefully explained and illustrated by well-chosen examples. He succeeds in putting a remarkable wealth of material into a 300-page book which will certainly serve as a basis for many courses on the subject."
Joachim Hilgert, Mathematical Reviews

From the Publisher