In the late 1950s, many of the more refined aspects of Fourier analysis were transferred from their original settings (the unit circle, the integers, the real line) to arbitrary locally compact abelian (LCA) groups. Rudin′s book, published in 1962, was the first to give a systematic account of these developments and has come to be regarded as a classic in the field. The basic facts concerning Fourier analysis and the structure of LCA groups are proved in the opening chapters, in order to make the treatment relatively self–contained.
Written by a master mathematical expositor, this classic text has served as a fundamental resource for over five decades. Initial chapters on the basic theorems of Fourier analysis and the structure of locally compact Abelian groups, together with appendixes on topology, topological groups, Banach spaces, Banach algebras, and measure theory, provide a self-contained treatment at the advanced undergraduate and graduate levels.
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