A Course in Abstract Harmonic Analysis - Textbooks in Mathematics (Hardback)Gerald B. Folland (author)
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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 algebrasIncludes Mark Kac's simple proof of a restricted form of Wiener's theoremExplains the relation between SU(2) and SO(3) in terms of quaternions, an elegant method that brings SO(4) into the picture with little effortDiscusses 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 entree to advanced mathematics, presenting the essentials of harmonic analysis on locally compact groups in a concise and accessible form.
Publisher: Taylor & Francis Inc
Number of pages: 305
Weight: 590 g
Dimensions: 235 x 156 mm
Edition: 2nd New edition
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 (R), Issue 98c
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