Clifford Algebras and Dirac Operators in Harmonic Analysis
Clifford Algebras and Dirac Operators in Harmonic Analysis
M. Murray, Virginia Polytechnic Institute and State University
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 all play a more fundamental role in Euclidean Fourier analysis than has been fully realized before. Their presentation of the Euclidean theory then links up naturally with the representation theory of semi-simple Lie groups. By keeping the treatment relatively simple, the book will be accessible to graduate students, yet the more advanced reader will also appreciate the wealth of results and insights made available here.
Reviews & endorsements
"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
Product details
August 2008Paperback
9780521071987
344 pages
229 × 152 × 20 mm
0.51kg
Available
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.
