Fourier Analysis on Groups

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. The Basic Theorems of Fourier Analysis.

The Structure of Locally Compact Abelian Groups.

Idempotent Measures.

Homomorphisms of Group Algebras.

Measures and Fourier Transforms on Thin Sets.

Functions of Fourier Transforms.

Closed Ideals in L?1(G).

Fourier Analysis on Ordered Groups.

Closed Subalgebras of L?1(G).

Appendices: Topology, Topological Groups, Banach Spaces, Banach Algebras, Measure Theory.

Bibliography.

List of Special Symbols.

Index.

Walter Rudin was an Austrian-American mathematician and professor of Mathematics at the University of Wisconsin-Madison.