Integration and Harmonic Analysis on Compact Groups

R. E. Edwards

doi:10.1017/CBO9780511662232

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.

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Contents

Frontmatter
pp i-ii
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Contents
pp iii-iv
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General Introduction
pp v-vi
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Acknowledgements
pp vi-vi
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Part 1 - Integration and the Riesz representation theorem
pp 1-41
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Part 2 - Harmonic analysis on compact groups
pp 42-162
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Appendix A
pp 163-174
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Appendix B
pp 175-178
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Bibliography
pp 179-184
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Integration and Harmonic Analysis on Compact Groups

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Contents

Frontmatter
pp i-ii

Contents
pp iii-iv

General Introduction
pp v-vi

Acknowledgements
pp vi-vi

Part 1 - Integration and the Riesz representation theorem
pp 1-41

Part 2 - Harmonic analysis on compact groups
pp 42-162

Appendix A
pp 163-174

Appendix B
pp 175-178

Bibliography
pp 179-184

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Integration and Harmonic Analysis on Compact Groups

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