Clifford Algebras and Dirac Operators in Harmonic Analysis

by J. Gilbert, M. Murray

Overview

The aim of this book is to unite the seemingly disparate topics of Clifford algebras, analysis on manifolds, and harmonic analysis. The authors show how algebra, geometry, and differential equations play a more fundamental role in Euclidean Fourier analysis. They then link their presentation of the Euclidean theory naturally to the representation theory of semi-simple Lie groups.

Product Details

ISBN-13:	9780521071987
Publisher:	Cambridge University Press
Publication date:	08/14/2008
Series:	Cambridge Studies in Advanced Mathematics , #26
Edition description:	Reissue
Pages:	344
Product dimensions:	6.00(w) x 8.90(h) x 0.90(d)

Table of Contents

1. Clifford algebras; 2. Dirac operators and Clifford analyticity; 3. Dirac operators and the spin group; 4. Dirac operators in the analysis on Euclidean space; 5. Dirac operators in representation theory; 6. Dirac operators in analysis.

Editorial Reviews

"All the topics covered in this book are worthwhile." John Ryan, Mathematical Reviews

"...contains a more-than-ample allotment of ideas and techniques that should be of great interest to a wide variety of analysts. The material itself is an attractive blend of algebra, analysis, and geometry. It is not particularly easy, but on the other hand, it is not impossibly difficult; and serious readers of this book should find it highly rewarding." Ray A. Kunze, Bulletin of the American Mathematical Society

From the Publisher