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

Part I. Symmetric Spaces. Harmonic Analysis on Spheres

1. General Considerations
Valery V. Volchkov, Vitaly V. Volchkov

2. Analogues of the Beltrami–Klein Model forRank One Symmetric Spaces ofNoncompactType
Valery V. Volchkov, Vitaly V. Volchkov

3. Realizations of Rank One Symmetric Spaces ofCompact Type
Valery V. Volchkov, Vitaly V. Volchkov

4. Realizations of the Irreducible Components ofthe Quasi-Regular Representation of Groups Transitive on Spheres. Invariant Subspaces
Valery V. Volchkov, Vitaly V. Volchkov

5. Non-Euclidean Analogues of Plane Waves
Valery V. Volchkov, Vitaly V. Volchkov

Part II. Transformations with Generalized Transmutation Property Associated with Eigenfunctions Expansions

6. Preliminaries
Valery V. Volchkov, Vitaly V. Volchkov

7. Some Special Functions
Valery V. Volchkov, Vitaly V. Volchkov

8. Exponential Expansions
Valery V. Volchkov, Vitaly V. Volchkov

9. Multidimensional Euclidean Case
Valery V. Volchkov, Vitaly V. Volchkov

10. The Case of Symmetric Spaces X=G/K ofNoncompact Type
Valery V. Volchkov, Vitaly V. Volchkov

11. The Case of Compact Symmetric Spaces
Valery V. Volchkov, Vitaly V. Volchkov

12. The Case of Phase Space
Valery V. Volchkov, Vitaly V. Volchkov

Part III. Mean Periodicity

13. Mean Periodic Functions on Subsets of the Real Line
Valery V. Volchkov, Vitaly V. Volchkov

14. Mean Periodic Functions on Multidimensional Domains
Valery V. Volchkov, Vitaly V. Volchkov

15. Mean Periodic Functions on G/K
Valery V. Volchkov, Vitaly V. Volchkov

16. Mean Periodic Functions on Compact Symmetric Spaces of Rank One
Valery V. Volchkov, Vitaly V. Volchkov

17. Mean Periodicity on Phase Space andtheHeisenberg Group
Valery V. Volchkov, Vitaly V. Volchkov

Part IV. Local Aspects of Spectral Analysis and the Exponential Representation Problem

18. A New Look at the Schwartz Theory
Valery V. Volchkov, Vitaly V. Volchkov

19. Recent Developments in the Spectral Analysis Problem for Higher Dimensions
Valery V. Volchkov, Vitaly V. Volchkov

20. ℰ′♮♮(X) Spectral Analysis on Domains ofNoncompact Symmetric Spaces of Arbitrary Rank
Valery V. Volchkov, Vitaly V. Volchkov

21. Spherical Spectral Analysis on Subsets ofCompact Symmetric Spaces
Valery V. Volchkov, Vitaly V. Volchkov

Keywords: Mathematics, Fourier Analysis, Integral Equations, Special Functions, Approximations and Expansions, Integral Transforms, Operational Calculus