A Course in Abstract Harmonic Analysis (Textbooks in Mathematics) - Hardcover

Folland, Gerald B.

Hardcover

ISBN 10: 0849384907 ISBN 13: 9780849384905

Publisher: CRC Press, 1994

Synopsis

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.

About this title

Review

"This delightful book fills a long-standing gap in the literature on abstract harmonic analysisTo the reviewer's knowledge, no one existing book contains al of the topics that are treated in this one[The author's] respect for the subject shows on every handthrough 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

Edition details

• Publisher: CRC Press
• Publication date: 1994
• Language: English
• ISBN 10: 0849384907
• ISBN 13: 9780849384905
• Binding: Hardcover
• Edition number: 1
• Number of pages: 288