Generalized spectral projections on symmetric spaces of noncompact type: Paley-Wiener theorems

Journal of Functional Analysis

Volumn 135, Issue 1, 1996, Pages 206-232

  Bray, William O ^a  

^a University of Maine   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030577618     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1996.0009     Document Type: Article

References (30)

1. 1. S. AGMON, A representation theorem for solutions of the Helmholtz equation and resolvent estimate of the Laplacian, in "Analysis et Cetera" (Rabinowitz and Zehnder, Eds.), Academic Press, San Diego, 1990.
2. 2. W. O. BRAY, A spectral Paley-Wiener theorem, Monatsh. Math. 116 (1993), 1-11.
3. 3. W. O. BRAY, Aspects of harmonic analysis on real hyperbolic space, in "Fourier Analysis: Analytic and Geometric Aspects," Lecture Notes in Pure and Appl. Math., Vol. 157 (W. O. Bray, P. S. Milojevic, and C. V. Stanojevic, Eds.), Dekker, New York, 1994.
4. 4. W. O. BRAY AND D. C. SOLMON, Paley-Wiener theorems on rank one symmetric spaces of non-compact type, Contemp. Math. 113 (1991).
5. 5. O. A. CAMPOLI, Paley-Wiener theorems on rank 1 semisimple Lie groups, Rev. Un. Mat. Argentina 29 (1980), 197-221.
6. p multipliers for noncompact symmetric spaces, Proc. Nat. Acad. Sci. U.S.A 71 (1974), 3911-3912.
7. 7. L. CLOZEL AND P. DELORME, Le théorème de Paley-Wiener invariant pour les groupes de Lie réductifs, Invent. Math. 77 (1984), 427-453.
8. 8. R. R. COIFMAN AND G. WEISS, "Analyse Harmonique Non-commutative sur Certains Espaces Homogènes," Lecture Notes in Math., Vol. 242, Springer-Verlag, New York/ Berlin, 1971.
9. 9. M. FLENSTED-JENSEN AND T. H. KOORNWINDER, Positive definite spherical functions on a non-compact rank one symmetric space, in "Analyse Harmonique sur les Groupes de Lie, II," Lecture Notes in Math, Vol. 739, Springer-Verlag, New York/Berlin, 1979.
10. 10. R. GANGOLLI AND V. S. VARADARAJAN, Harmonic analysis of spherical functions on real reductive groups, Ergeb. Math. Grenzgeb. 101 (1988).
11. 11. S. HELGASON, A duality for symmetric spaces with applications to group representations, I, Adv. Math. 5 (1970), 1-154; II, Adv. Math. 22 (1976), 197-219.
12. 11. S. HELGASON, A duality for symmetric spaces with applications to group representations, I, Adv. Math. 5 (1970), 1-154; II, Adv. Math. 22 (1976), 197-219.
13. 12. S. HELGASON, The surjectivity of invariant differential operators on symmetric spaces, Ann. of Math. 98 (1973), 457-479.
14. 13. S. HELGASON, Eigenspaces of the Laplacian, integral representations, and irreducibility, J. Funct. Anal. 17 (1974), 328-353.
15. 14. S. HELGASON, "Differential Geometry, Lie Groups, and Symmetric Spaces," Academic Press, New York, 1978.
16. 15. S. HELGASON, "Groups and Geometric Analysis," Academic Press, New York, 1984.
17. 16. S. HELGASON, Some results on Radon transforms, Huygen's principal, and x-ray transforms, Contemp. Math. 63 (1987).
18. 17. F. JOHN, "Plane Waves and Spherical Means Applied to Partial Differential Equations," Springer-Verlag, 1955.
19. 18. K. D. JOHNSON, Composition series and intertwining operators for the spherical principal series, II, Transf. Amer. Math. Soc. 215 (1976), 269-283.
20. 19. K. D. JOHNSON AND N. WALLACH, Composition series and intertwining operators for the spherical principal series, I, Trans. Am. Math. Soc. 229 (1977), 137-174.
21. 20. T. KAWAZOE, An analogue of Paley-Wiener theorem on rank 1 semisimple Lie groups, I and II, Tokyo J. Math. 2 (1979), 397-407, 409-421.
22. 21. T. H. KOORNWINDER, Jacobi functions and analysis on non-compact semisimple Lie groups, in "Special Functions: Group Theoretical Aspects and Applications" (R. Askey, T. H. Koornwinder, and W. Schempp, Eds.), Reidel, Dordrecht, 1984.
23. 22. B. KOSTANT, On the existence and irreducibility of certain series of representations, Bull. Amer. Math. Soc. 75 (1969), 627-642.
24. 23. J. ORLOFF, Invariant Radon transforms on a symmetric space, Tran. Amer. Math. Soc. 318 (1990), 581-600.
25. p(G/K), 1 ≤ p < 2, Proc. Amer. Math. Soc. 73, No. 3 (1979), 398-404.
26. 25. E. M. STEIN AND G. WEISS, "Introduction to Fourier Analysis on Euclidean Spaces," Princeton Univ. Press, Princeton, 1971.
27. 26. R. S. STRICHARTZ, Harmonic analysis as spectral theory of Laplacians, J. Funct. Anal. 87 (1989), 51-148.
28. 27. R. S. STRICHARTZ, correction to [18], J. Funct. Anal. 109 (1992), 457-460.
29. 28. R. S. STRICHARTZ, Local harmonic analysis on spheres, J. Funct. Anal. 77 (1988), 403-433.
30. p harmonic analysis and Radon transforms on the Heisenberg group, J. Funct. Anal. 96 (1991), 350-406.