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.
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