Product Description
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.

	Preface
1	Banach Algebras and Spectral Theory	1
2	Locally Compact Groups	31
3	Basic Representation Theory	67
4	Analysis on Locally Compact Abelian Groups	87
5	Analysis on Compact Groups	125
6	Induced Representations	151
7	Further Topics in Representation Theory	201
	App. 1 A Hilbert Space Miscellany	253
	App. 2 Trace-Class and Hilbert-Schmidt Operators	256
	App. 3 Vector-Valued Integrals	259
	Bibliography	263
	Index	271
	List of Figures