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...

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...