A Course in Abstract Harmonic Analysis

Gerald B. Folland

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English

Chapman & Hall/CRC
14 October 2024

Calculus & mathematical analysis

Series: Textbooks in Mathematics

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 results and techniques that are of interest in their own right.

This book develops the abstract theory along with a well-chosen selection of concrete examples that exemplify the results and show the breadth of their applicability. After a preliminary chapter containing the necessary background material on Banach algebras and spectral theory, the text sets out the general theory of locally compact groups and their unitary representations, followed by a development of the more specific theory of analysis on Abelian groups and compact groups. There is an extensive chapter on the theory of induced representations and its applications, and the book concludes with a more informal exposition on the theory of representations of non-Abelian, non-compact groups.

Featuring extensive updates and new examples, the Second Edition:

Adds a short section on von Neumann algebras Includes Mark Kac’s simple proof of a restricted form of Wiener’s theorem Explains the relation between SU(2) and SO(3) in terms of quaternions, an elegant method that brings SO(4) into the picture with little effort Discusses representations of the discrete Heisenberg group and its central quotients, illustrating the Mackey machine for regular semi-direct products and the pathological phenomena for nonregular ones

A Course in Abstract Harmonic Analysis, Second Edition serves as an entrée to advanced mathematics, presenting the essentials of harmonic analysis on locally compact groups in a concise and accessible form.

By: Gerald B. Folland
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Edition: 2nd edition
Dimensions: Height: 234mm, Width: 156mm,
Weight: 589g
ISBN: 9781032922218
ISBN 10: 1032922214
Series: Textbooks in Mathematics
Pages: 320
Publication Date: 14 October 2024
Audience: College/higher education , Primary
Format: Paperback
Publisher's Status: Active

Banach Algebras and Spectral Theory. Locally Compact Groups. Basic Representation Theory. Analysis on Locally Compact Abelian Groups. Analysis on Compact Groups. Induced Representations. Further Topics in Representation Theory. Appendices.

Gerald B. Folland received his Ph.D in mathematics from Princeton University, New Jersey, USA in 1971. After two years at the Courant Institute of Mathematical Sciences, New York, USA, he joined the faculty of the University of Washington, Seattle, USA, where he is now professor emeritus of mathematics. He has written a number of research and expository articles on harmonic analysis and its applications, and he is the author of eleven textbooks and research monographs.

Reviews for A Course in Abstract Harmonic Analysis

"Praise for the Previous Edition ""This delightful book fills a long-standing gap in the literature on abstract harmonic analysis. … To the reviewer's knowledge, no one existing book contains all of the topics that are treated in this one. … [The author's] respect for the subject shows on every hand…through his careful writing style, which is concise, yet simple and elegant. The reviewer would encourage anyone with an interest in harmonic analysis to have this book in his or her personal library. … a fine book that the reviewer would have been proud to write."" —Robert S. Doran in Mathematical Reviews®, Issue 98c"

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A Course in Abstract Harmonic Analysis

Gerald B. Folland

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