Abstract Harmonic Analysis: Structure and Analysis, Vol.2 Volume 2

This book is a continuation of vol. I (Grundlehren vol. 115, also available in softcover), and contains a detailed treatment of some important parts of harmonic analysis on compact and locally compact abelian groups. From the reviews: "This work aims at giving a monographic presentation of abstract harmonic analysis, far more complete and comprehensive than any book already existing on the subject ... in connection with every problem treated the book offers a many-sided outlook and leads up to most modern developments. Carefull attention is also given to the history of the subject, and there is an extensive bibliography ... the reviewer believes that for many years to come this will remain the classical presentation of abstract harmonic analysis." Publicationes Mathematicae Volume one. The book is based on courses given by E. HEWITT at the University of Washington and the University of Uppsala, although naturally the material of these courses has been enormously expanded to meet the needs of a formal monograph. Like the other treatments of harmonic analysis that have appeared since 1940, the book is a lineal descendant of A. WEIL's fundamental treatise (WEIL [ 4]) 1. The debt of all workers in the field to WEIL's work is well known and enormous. We have also borrowed freely from Loomis’s treatment of the subject (Loomis [2]), from NAIMARK [1], and most especially from Pontryagin [7]. In our exposition of the structure of locally compact Abelian groups and of the Pontryagin-van Kampen duality theorem, we have been strongly influenced by Pontryagin's treatment. We hope to have justified the writing of yet another treatise on abstract harmonic analysis by taking up recent work, by writing out the details of every important construction and theorem, and by including a large number of concrete examples and facts not available in other textbooks V. 1. Structure Of Topological Groups, Integration Theory, Group Representations -- V. 2. Structure And Analysis For Compact Groups, Analysis On Locally Compact Abelian Groups. By Edwin Hewitt And Kenneth A. Ross. Cover Title, V. 1: Abstract Harmonic Analysis I. Cover Title, V. 2: Abstract Harmonic Analysis Ii. Includes Bibliographies And Indexes.