Sampling of Paley-Wiener functions on stratified groups
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We consider a generalization of entire functions of spherical exponential type on stratified groups. An analog of the Paley-Wiener theorem is given. We also show that every spectral entire function on a stratified group is uniquely determined by its values on some discrete subgroups. The main result of the article is reconstruction formula of spectral entire functions from their values on discrete subgroups using Lagrangian splines.
Math Subject ClassificationsPrimary 43A80 secondary 41A15, 41A17 Keywords and Phrases Stratified group sub-Laplacian Bernstein inequality Lagrangian spline
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- Benedetto, J. (1992). Irregular sampling and frames, inWavelets: A Tutorial in Theory and Applications, Chui, C.K. Ed., Academic Press, Boston, 445–507.Google Scholar
- Krein, S. and Pesenson, I. (1990)Interpolation Spaces and Approximation on Lie Groups, The Voronezh State University, Voronezh, (in Russian), 200.Google Scholar
- Lions, J.-L. and Magenes, E. (1975),Non-Homogeneous Boundary Value Problem and Applications, Springer-Verlag.Google Scholar
- Pesenson, I. (1990). The Bernstein Inequality in the Space of Representation of Lie group.Dokl. Acad. Nauk USSR, 313(4), 86–90; English translation inSoviet Math. Dokl., 42, (1991).Google Scholar
- Pesenson, I. (1995).Lagrangian Splines, Spectral Entire Functions and Shannon-Whittaker Theorem on Manifolds, Temple University Research Report 95-87, 1–28.Google Scholar
- Pesenson, I. (1996). A sampling theorem on homogeneous manifolds, submitted.Google Scholar