Classical Harmonic Analysis and Locally Compact Groups / Edition 2

by Hans Reiter, Jan D. Stegeman

Overview

A revised and expanded second edition of Reiter's classic text Classical 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.

Product Details

ISBN-13:	9780198511892
Publisher:	Oxford University Press
Publication date:	01/25/2001
Series:	London Mathematical Society Monographs , #22
Edition description:	REV
Pages:	344
Product dimensions:	9.00(w) x 6.00(h) x 0.90(d)

About the Author

University of Vienna

University of Utrecht

Table of Contents

Reader's guide1. Classical harmonic analysis and Wiener's theorem2. Function algebras and the generalization of Wiener's theorem3. Locally compact groups and the Haar measure4. Locally compact abelian groups and the foundations of harmonic analysis5. Functions on locally compact abelian groups6. Wiener's theorem and locally compact abelian groups7. The spectrum and its applications8. Functions on general locally compact groupsA. Additional materialB. Notes and additional referencesReferencesSummary of notationsSubject index

Editorial Reviews

"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 background of real and complex analysis."—EMS

"[Stegman] excellently succeeded in preparing this new edition in the spirit of Reiter... [a] very recommendable book."—Mathematical Abstracts

"On the whole this book is very good and had interesting material to go through for beginners on harmonic analysis."—Mathematical Reviews

". . .I can recommend [this book] both to those who want a careful account of the foundations of the subject, and to those who want to dip into it to find examples of what can go wrong and right in classical harmonic analysis."—Bulletin of the London Mathematical Society

From the Publisher

When Reiter (1921-92) was writing the 1968 edition, Stegeman (Utrecht U.) was his assistant and student, and contributed somewhat to its final form. He has added some new material, mostly in two appendices; and more recent references, though he retained all old ones and distinguish between them with a symbol. He also abandoned the original format of printing proofs and more technical matters apart from the main text, and sometimes in a smaller type. The general survey and detailed exposition proceeds from particular cases to general results, from classical theorems to more recent ones. Abstract concepts are illustrated by examples. An attempt has been made to keep the underlying reasoning clearly visible through the technical details of the formal exposition of proofs. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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