Integration and Harmonic Analysis on Compact Groups Book

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.