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Integration and Harmonic Analysis on Compact Groups : London Mathematical Society Lecture Notes - R. E. Edwards

Integration and Harmonic Analysis on Compact Groups

London Mathematical Society Lecture Notes

Paperback Published: 6th November 1972
ISBN: 9780521097178
Number Of Pages: 192

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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."

General Introduction
Integration and the Riesz representation theorem
Preliminaries regarding measures and integrals
Statement and discussion of Riesz's theorem
Method of proof of RRT: preliminaries
First stage of extension of I
Second stage of extension of I
The space of integrable functions
The a- measure associated with I: proof of the RRT
Lebesgue's convergence theorem
Concerning the necessity of the hypotheses in the RRT
Historical remarks
Complex-valued functions
Harmonic analysis on compact groups
Invariant integration
Group representations
The Fourier transform
The completeness and uniqueness theorems
Schur's lemma and its consequences
The orthogonality relations
Fourier series in L2(G)
Positive definite functions
Summability and convergence of Fourier series
Closed spans of translates
Structural building bricks and spectra
Closed ideals and closed invariant subspaces
Spectral synthesis problems
The Hausdorff-Young theorem
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521097178
ISBN-10: 0521097177
Series: London Mathematical Society Lecture Notes
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 192
Published: 6th November 1972
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 1.12
Weight (kg): 0.29