A Course in Abstract Harmonic Analysis

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CRC Press, Dec 27, 1994 - Mathematics - 288 pages
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Abstract theory remains an indispensable foundation for the study of concrete cases. It shows what the general picture should look like and provides results that are useful again and again. Despite this, however, there are few, if any introductory texts that present a unified picture of the general abstract theory.

A Course in Abstract Harmonic Analysis offers a concise, readable introduction to Fourier analysis on groups and unitary representation theory. After a brief review of the relevant parts of Banach algebra theory and spectral theory, the book proceeds to the basic facts about locally compact groups, Haar measure, and unitary representations, including the Gelfand-Raikov existence theorem. The author devotes two chapters to analysis on Abelian groups and compact groups, then explores induced representations, featuring the imprimitivity theorem and its applications. The book concludes with an informal discussion of some further aspects of the representation theory of non-compact, non-Abelian groups.
  

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Contents

Banach Algebras and Spectral Theory
1
Locally Compact Groups
31
Basic Representation Theory
67
Analysis on Locally Compact Abelian Groups
87
Analysis on Compact Groups
125
Induced Representations
151
Further Topics in Representation Theory
201
Appendices
253
Bibliography
263
Index
271
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