Hans Reiter – författare

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 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 of 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.

These notes give an account of recent work in harmonic analysis dealing with the analytical foundations of A. Weil''s theory of metaplectic groups. It is shown that Weil''s main theorem holds for a class of functions (a certain Segal algebra) larger than that of the Schwartz-Bruhat functions considered by Weil. The theorem is derived here from some general results about this class which seems to be a rather natural one in the context of Weil''s theory. No previous knowledge of the latter is assumed, however, and the theory is developed here, step by step; Further, a complete discussion of the Segal algebra concerned is given, with references to the literature. Weil''s metaplectic groups are somewhat easier to investigate when the characteristic is not 2; the case of characteristic 2 presents some special features which are fully discussed. New problems that arise are indicated.

These notes give an account of recent work in harmonic analysis dealing with the analytical foundations of A. Weil's theory of metaplectic groups. It is shown that Weil's main theorem holds for a class of functions (a certain Segal algebra) larger than that of the Schwartz-Bruhat functions considered by Weil. The theorem is derived here from some general results about this class which seems to be a rather natural one in the context of Weil's theory. No previous knowledge of the latter is assumed, however, and the theory is developed here, step by step; Further, a complete discussion of the Segal algebra concerned is given, with references to the literature. Weil's metaplectic groups are somewhat easier to investigate when the characteristic is not 2; the case of characteristic 2 presents some special features which are fully discussed. New problems that arise are indicated.

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.