Clifford Algebras and Dirac Operators in Harmonic Analysis

The aim of this book is to unite the seemingly disparate topics of Clifford algebras, analysis on manifolds and harmonic analysis.

J. Gilbert (Author), M. Murray (Author)

9780521071987, Cambridge University Press

Paperback / softback, published 14 August 2008

344 pages
22.9 x 15.2 x 2 cm, 0.51 kg

"...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

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.

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.

Subject Areas: Calculus & mathematical analysis [PBK]