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Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Groups

Valey V. Volchkov and Vitaly V. Volchkov
Publication Date: 
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Springer Monographs in Mathematics
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Part 1; Symmetric Spaces. Harmonic Analysis on Spheres.- 1. General Considerations.- 2. Analogues of the Beltrami-Klein Model for Rank One Symmetric Spaces of Non-Compact Type.- 3. Realizations of Rank One Symmetric Spaces of Compact Type.- 4. Realizations of the Irreducible Components of the Quasi-Regular Representation of Groups Transitive on Spheres. Invariant Subspaces.- 5. Non-Euclidean Analogues of Plane Waves.- Comments, Further Results and Open Problems.- Part 2; Transformations with Generalized Transmutation Property Associated with Eigenfunctions Expansions.- 6. Preliminaries.- 7. Some Special Functions.- 8. Exponential Expansions.- 9. Multidimensional Euclidean Case.- 10. The Case of Symmetric Spaces X = G/K of Noncompact Type.- 11. The Case of Compact Symmetric Spaces.- 12. The Case of Phase Space.- Comments, Further Results and Open Problems.- Part 3; Mean periodicity.- 13. Mean Periodic Functions on Subsets of the Real Line.- 14. Mean Periodic Functions on Multidimensional Domains.- 15. Mean Periodic Functions on G/K.- 16. Mean Periodic Functions on Compact Symmetric Spaces of Rank One.- 17. Mean Periodicity on Phase Space and the Heisenberg Group.- Comments, Further Results and Open Problems.- Part 4. Local Aspects of Spectral Analysis and the Exponential Representation Problem.- 18. A New Look at the Schwartz Theory.- 19. Recent Developments in the Spectral Analysis Problem for Higher Dimensions.- 20. Spectral Analysis on Domains of Noncompact Symmetric Spaces of an Arbitrary Rank.- 21. Spherical Spectral Analysis on Subsets of Compact Symmetric Spaces.- Comments, Further Results and Open Problems.- Bibliography.