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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.

Algebra --- Harmonic analysis. Fourier analysis --- Clifford algebras. --- Dirac equation. --- Harmonic analysis --- Harmonic analysis.