Cover image for Integration and harmonic analysis on compact groups
Title:
Integration and harmonic analysis on compact groups
Personal Author:
Series:
Lecture notes series (London Mathematical Society); 8
Publication Information:
London : Cambridge Univ. Pr., 1972
ISBN:
9780521097178

Available:*

Library
Item Barcode
Call Number
Material Type
Item Category 1
Status
Searching...
30000001818339 QA387 .E38 1972 Open Access Book Book
Searching...

On Order

Summary

Summary

These notes provide a reasonably self-contained introductory survey of certain aspects of harmonic analysis on compact groups. The first part of the book seeks to give a brief account of integration theory on compact Hausdorff spaces. The second, larger part starts from the existence and essential uniqueness of an invariant integral on every compact Hausdorff group. Topics subsequently outlined include representations, the Peter-Weyl theory, positive definite functions, summability and convergence, spans of translates, closed ideals and invariant subspaces, spectral synthesis problems, the Hausdorff-Young theorem, and lacunarity.


Table of Contents

General Introduction
Acknowledgements
Part I Integration and the Riesz representation theorem
1 Preliminaries regarding measures and integrals
2 Statement and discussion of Riesz's theorem
3 Method of proof of RRT: preliminaries
4 First stage of extension of I
5 Second stage of extension of I
6 The space of integrable functions
7 The a- measure associated with I: proof of the RRT
8 Lebesgue's convergence theorem
9 Concerning the necessity of the hypotheses in the RRT
10 Historical remarks
11 Complex-valued functions
Part II Harmonic analysis on compact groups
12 Invariant integration
13 Group representations
14 The Fourier transform
15 The completeness and uniqueness theorems
16 Schur's lemma and its consequences
17 The orthogonality relations
18 Fourier series in L2(G)
19 Positive definite functions
20 Summability and convergence of Fourier series
21 Closed spans of translates
22 Structural building bricks and spectra
23 Closed ideals and closed invariant subspaces
24 Spectral synthesis problems
25 The Hausdorff-Young theorem
26 Lacunarity