These notes provide a reasonably self-contained introductory survey of certain aspects of harmonic analysis on compact groups.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
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.
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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