Clifford Algebras and Dirac Operators in Harmonic Analysis (Cambridge Studies in Advanced Mathematics, Series Number 26)

This book is helping me a lot with my Ph.D. dissertation. It includes a lot of important results on hypercomplex analysis not usually found in the standard monographs on the subject (Brackx, Gürlebeck, Shapiro,...). Its contents are: Clifford algebras, Dirac operators and Clifford analyticity, representations of Spin(V,Q), constant coefficient operators of Dirac type, Dirac operators and manifolds. Presents motivation for each section and extensive references. A must-reading to become a speciallist in this area. Suitable for graduate students and researchers. Please read the rest of my reviews (just click on my name above). 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.

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.