Fourier Analysis on Groups
Fourier Analysis on Groups by Walter Rudin, published by Courier Dover Publications on April 19, 2017, is a comprehensive text that delves into the field of Fourier analysis. This edition, consisting of 286 pages, is written in English and is designed for advanced undergraduate and graduate students. The book reflects the significant research developments in Fourier analysis that occurred in the decade leading up to its first publication in 1962.
Readers will find a self-contained exploration of essential theorems of Fourier analysis and the structure of locally compact Abelian groups. The text covers various topics, including idempotent measures, homomorphisms of group algebras, and Fourier transforms on thin sets. Additionally, helpful appendices provide background information on topology, Banach spaces, and measure theory, making this work a valuable resource for those studying mathematics, group theory, and mathematical analysis.
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Written by a master mathematical expositor, this classic text reflects the results of the intense period of research and development in the area of Fourier analysis in the decade preceding its first publication in 1962. The enduringly relevant treatment is geared toward advanced undergraduate and graduate students and has served as a fundamental resource for more than five decades.
The self-contained text opens with an overview of the basic theorems of Fourier analysis and the structure of locally compact Abelian groups. Subsequent chapters explore idempotent measures, homomorphisms of group algebras, measures and Fourier transforms on thin sets, functions of Fourier transforms, closed ideals in L1(G), Fourier analysis on ordered groups, and closed subalgebras of L1(G). Helpful Appendixes contain background information on topology and topological groups, Banach spaces and algebras, and measure theory.
Dover (2017) republication of the edition originally published by Interscience Publishers, New York, 1962.
www.doverpublications.com
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