Classical harmonic analysis and locally compact groups / Hans Reiter

This book is one of the very few books on harmonic analysis that makes for pleasant reading and is at the same time rigorous and very informative. Moreover, many open problems are raised. The basic principles from classical Fourier analysis that inspired some deep generalisations to harmonic analysis are given clearly at the very beginning. The author also discusses amenability in locally compact groups and shows how the basic theorems on amenability of a locally compact group are intimately related to approximation techniques of harmonic analysis that have been used by workers such as W. Rudin [Fourier analysis on groups, Interscience, New York, 1962; MR0152834), A. Weil (L'intégration dans les groupes topologiques et ses applications, second edition, Actualités Sci. Indust., No. 1145, Hermann, Paris, 1951), C. Herz (Trans. Amer. Math. Soc. 94 (1960), 181–232; MR0131779) and others in the field. This book covers much material which is not found in recent books in that area, such as the cited book of Rudin and Abstract harmonic analysis, by E. Hewitt and K. A. Ross (Vol. I: Structure of topological groups. Integration theory, group representations, Academic Press, New York, 1963; MR0156915; Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups, Springer, New York, 1970; MR0262773. The present work clearly sets forth the principle of relativisation and the important role it plays in the development of the entire subject. (MathSciNet)

Bibliogr. p. [190]-195. Liste des notations. Index