Integration and Harmonic Analysis on Compact Groups

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.

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