
A Course in Abstract Harmonic Analysis
Gerald B. Folland(Author)
Chapman & Hall/CRC (Publisher)
2nd Edition
Published on 25. September 2015
Book
Hardback
320 pages
978-1-4987-2713-6 (ISBN)
Description
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 entree to advanced mathematics, presenting the essentials of harmonic analysis on locally compact groups in a concise and accessible form.
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 entree to advanced mathematics, presenting the essentials of harmonic analysis on locally compact groups in a concise and accessible form.
Reviews / Votes
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
More details
Series
Edition
2nd edition
Language
English
Place of publication
Boca Raton
United States
Publishing group
Taylor & Francis Inc
Target group
College/higher education
Postgraduate
Illustrations
3 s/w Abbildungen
3 Illustrations, black and white
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 22 mm
Weight
649 gr
ISBN-13
978-1-4987-2713-6 (9781498727136)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

Gerald B. Folland
A Course in Abstract Harmonic Analysis
Book
10/2024
2nd Edition
Chapman & Hall/CRC
€81.50
Shipment within 10-20 days

Gerald B. Folland
A Course in Abstract Harmonic Analysis
E-Book
02/2016
2nd Edition
Chapman & Hall/CRC
€78.99
Available for download

Gerald B. Folland
A Course in Abstract Harmonic Analysis
E-Book
02/2016
2nd Edition
Chapman and Hall
€78.99
Available for download
Previous edition

Gerald B. Folland
A Course in Abstract Harmonic Analysis
Book
12/1994
1st Edition
CRC Press
€146.08
Article exhausted; check for reprint
Person
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.
Content
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.