Classical Harmonic Analysis and Locally Compact Groups [Hardcover]

A revised and expanded second edition of Reiter's classic textClassical Harmonic Analysis and Locally Compact Groups(Clarendon Press 1968). It deals with various developments in analysis centring around around the fundamental work of Wiener, Carleman, and especially A. Weil. It starts with the classical theory of Fourier transforms in euclidean space, continues with a study at certain general function algebras, and then discusses functions defined on locally compact groups. The aim is, firstly, to bring out clearly the relations between classical analysis and group theory , and secondly, to study basic properties of functions on abelian and non-abelian groups. The book gives a systematic introduction to these topics and endeavours to provide tools for further research. In the new edition relevant material is added that was not yet available at the time of the first edition.

Reader's guide
1. Classical harmonic analysis and Wiener's theorem
2. Function algebras and the generalization of Wiener's theorem
3. Locally compact groups and the Haar measure
4. Locally compact abelian groups and the foundations of harmonic analysis
5. Functions on locally compact abelian groups
6. Wiener's theorem and locally compact abelian groups
7. The spectrum and its applications
8. Functions on general locally compact groups
A. Additional material
B. Notes and additional references
References
Summary of notations
Subject index

The original book, Classical harmonic analysis and locally compact groups, by H. Reiter appeared in 1968. . . the new addition has expanded and additional material has been appended. . .The monograph is designed to serve both as a general survey and a s a detailed exposition of the topics it treats. It should be accessible to graduate students and researchers interested in harmonic analysis and understandable with a basic knowledge of functional analysis and measure theory, together with a backgrlc¬