A Course In Abstract Harmonic Analysis
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A Course in Abstract Harmonic Analysis
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.
A Course in Abstract Harmonic Analysis
A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant resul
Principles of Harmonic Analysis
This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.