Fourier Analysis on Groups - (Dover Books on Mathematics) by Walter Rudin (Paperback)

This comprehensive and self-contained textbook on Fourier Analysis is a must-read for advanced undergraduate and graduate students, as well as researchers in the field.

Written by a master mathematical expositor, it provides an overview of the basic theorems of Fourier analysis and the structure of locally compact Abelian groups, before delving into more specialized topics such as idempotent measures, homomorphisms of group algebras, and closed ideals in L1(G).

The book's helpful appendices contain background information on topology and topological groups, Banach spaces and algebras, and measure theory.

With its broad scope and depth of coverage, this text has served as a fundamental resource for more than five decades and continues to be an essential tool for anyone working in the field of Fourier analysis.