Poincaré-Type inequalities and reconstruction of Paley-Wiener functions on manifolds

Journal of Geometric Analysis

Volumn 14, Issue 1, 2004, Pages 101-121

  Pesenson, Isaac ^a  

^a Temple University   (United States)

Author keywords

band limited functions on manifolds; Laplace Beltrami operator; Poincar inequality on manifolds; sampling theorem on manifolds; splines on manifolds

Indexed keywords

EID: 84867930720     PISSN: 10506926     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02921868     Document Type: Article

References (18)

1. Benedetto, J.J.Irregular Sampling and Frames, Academic Press, Boston, 445-507, (1992).
2. J. Cheeger M. Gromov M. Taylor 1982 Finite propagation speed, kernel estimates for functions of the Laplace operator and the geometry of complete Riemannian manifolds J. Diff. Geom. 17 15 53 658471 0493.53035
3. Feichtinger, H. and Grochenig, K. Theory and practice of irregular sampling. Wavelets: mathematics and applications,Stud. Adv. Math.; 305-363, CRC Press, Boca Raton, FL, (1994).
4. Hebey, E.Sobolev Spaces on Riemannian Manifolds, Springer-Verlag, Berlin, Heidelberg, (1996).
5. Krein, S. and Pesenson, I.Interpolation Spaces and Approximation on Lie Groups, The Voronezh State University, Voronezh, (1990), (Russian).
6. Lions, J.L. and Magenes, E.Non-Homogeneous Boundary Value Problem and Applications, Springer-Verlag, (1975).
7. P. Maheux L. Saloff-Coste 1995 Analyse sur les boules d'un operateur sous-elliptique Math. Annal. 303 301 324 10.1007/BF01461013 1359957
8. I. Pesenson 1988 The best approximation in a representation space of a Lie group Dokl. Acad. Nauk USSR 302 5 1055 1059
9. I. Pesenson 1990 The Bernstein inequality in the space of representation of Lie group Dokl. Acad. Nauk USSR 313 86 90
10. Pesenson, I.Lagrangian Splines, Spectral Entire Functions and Shannon-Whittaker Theorem on Manifolds, Temple University, Research Report, 95-87, 1-28, (1995).
11. I. Pesenson 1998 Reconstruction of Paley-Wiener functions on the Heisenberg group Am. Math. Soc. Transl. 184 2 207 216 1729935
12. I. Pesenson 1998 Sampling of Paley-Wiener functions on stratified groups J. Fourier Anal. Appl. 4 3 271 281 10.1007/BF02476027 1650917 0930.43009
13. d) Proceed. of AMS 127 12 3593 3600 10.1090/S0002-9939-99-04938-2 1610773 0998.42024
14. I. Pesenson 2000 A sampling theorem on homogeneous manifolds Trans. AMS 352 9 4257 4270 10.1090/S0002-9947-00-02592-7 1707201 0976.43004
15. I. Pesenson 2001 Sampling of band limited vectors J. Fourier Anal. Appl. 7 1 93 100 10.1007/s00041-001-0007-9 1812998 0998.42025
16. J. Roe 1988 An index theorem on open manifolds J. Diff. Geom. 27 87 113 918459
17. Schoenberg, I. Cardinal spline interpolation,CBMS,12, SIAM, Philadelphia, (1973).
18. R. Strichartz 1983 Analysis of the Laplacian on the complete Riemannian manifold J. Funct. Anal. 52 48 79 10.1016/0022-1236(83)90090-3 705991 0515.58037