Classical Harmonic Analysis and Locally Compact Groups (London Mathematical Society Monographs, 22)

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.

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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)