Clifford Algebras and Dirac Operators in Harmonic Analysis
Clifford Algebras and Dirac Operators in Harmonic Analysis by John E. Gilbert, published by Cambridge University Press on July 26, 1991, is a comprehensive exploration of the connections between Clifford algebras, analysis on manifolds, and harmonic analysis. This edition spans 334 pages and is presented in English, offering a detailed examination of how algebra, geometry, and differential equations contribute to the understanding of Euclidean Fourier analysis.
Readers will find that the book presents a cohesive framework that integrates various mathematical concepts, illustrating their interrelationships. The text delves into the representation theory of semi-simple Lie groups, providing insights into advanced topics in mathematics such as linear algebra, calculus, and differential equations. This scholarly work serves as a resource for those interested in the mathematical foundations underlying harmonic analysis and its applications.
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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.
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