Fourier Analysis on Groups (Google eBook)

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John Wiley & Sons, Sep 9, 2011 - Mathematics - 296 pages
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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.
  

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Contents

Chapter 1 The Basic Theorems of Fourier Analysis
1
Chapter 2 The Structure of Locally Compact Abelian Groups
35
Chapter 3 Idempotent Measures
59
Chapter 4 Homomorphisms of Group Algebras
77
Chapter 5 Measures and Fourier Transforms on Thin Sets
97
Chapter 6 Functions of Fourier Transforms
131
Chapter 7 Closed Ideals in L1 G
157
Chapter 8 Fourier Analysis on Ordered Groups
193
Chapter 9 Closed Subalgebras of L1G
231
Appendices
247
Bibliography
271
List of Special Symbols
281
Index
283
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