A sampling theorem on homogeneous manifolds

Transactions of the American Mathematical Society

Volumn 352, Issue 9, 2000, Pages 4257-4269

  Pesenson, Isaac ^a  

^a Temple University   (United States)

Author keywords

Lagrangian splines; Laplace Beltrami operator; Manifold; Shannon whittaker formula; Sobolev spaces; Spectral entire functions

Indexed keywords

EID: 23044519949     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-00-02592-7     Document Type: Article

References (13)

1. J. Benedetto, Irregular sampling and frames, Wavelets: A tutorial in Theory and Applications (C.K.Chui, ed.), Academic Press, Boston, 1992, pp. 445-507. MR 93c:42030
2. J. Cheeger, M. Gromov, M. Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator and the geometry of complete Riemannian manifolds, J. Diff. Geom. 17 (1982), 15-53. MR 84b:58109
3. S. Krein, I. Pesenson, Interpolation Spaces and Approximation on Lie Groups, The Voronezh State University, Voronezh, 1990, (Russian).
4. P. Lemarie, Bases d'ondeletts sur les gropes stratifies, Bull. Soc. Math. France, 117 (1989), 211-232. MR 90j:42066
5. J.- L. Lions, E. Magenes, Non-Homogeneous Boundary Value Problem and Applications, Springer-Verlag, 1975.
6. Y. Lyubarskii, W. R. Madych, The Recovery of Irregularly Sampled Band Limited Functions via Tempered Splines, J. of Functional Analysis 125 (1994), 201-222. MR 96d:41013
7. I. Pesenson, The Bernstein Inequality in the Space of Representation of Lie group, Dokl. Akad. Nauk USSR 313 (1990), 86-90; English transi, in Soviet Math. Dokl. 42 (1991). MR 92j:43010
8. I. Pesenson, Reconstruction of Paley-Wiener functions on the Heisenberg group, Translations of AMS (to appear).
9. I. Pesenson, Sampling of Paley-Wiener functions on stratified groups, J. of Fourier Analysis and Applications 4 (1998), 269-280. MR 99j:41024
10. J. Roe, An index theorem on open manifolds. I, II, J. Diff. Geom. 27 (1988), 87-113, 115-136. MR 89a:58102
11. I. Schoenberg, Cardinal Spline Interpolation, CBMS, 12, SIAM, Philadelphia, 1973. MR 54:8095
12. M. Shubin, Spectral theory of elliptic operators on non-compact manifolds, S.M.F. Asterisque 207 (1992), 35-108. MR 94h:58175
13. R. Strichartz, Analysis of the Laplacian on the complete Riemannian Manifold, J. Funct. Anal. 52 (1983), 48-79. MR 84m:58138