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  3. Clifford Algebras and Dirac Operators in Harmonic Analysis
  • Cited by 365
  • J. Gilbert, University of Texas, Austin, M. Murray, Virginia Polytechnic Institute and State University
Publisher:
Cambridge University Press
Online publication date:
November 2009
Print publication year:
1991
Online ISBN:
9780511611582
DOI:
https://doi.org/10.1017/CBO9780511611582
Subjects:
Mathematics (general), Mathematics, Mathematical Physics, Abstract Analysis
Series:
Cambridge Studies in Advanced Mathematics (26)
Information

Book description

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

"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

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