Description:
This book presents the essentials of harmonic analysis on locally compact groups in a concise and accessible form. The text provides necessary background on Banach algebras and spectral theory, develops the theory of analysis on Abelian groups and compact groups, examines the theory of induced representations, and explores the theory of representations of non-Abelian, non-compact groups. This second edition adds material on representations of the discrete Heisenberg group, coverage of von Neumann algebras and Wiener's theorem, and discussion of SU(2), SO(3), and SO(4) using quaternions.
Review Quotes:
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