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A sampling theorem on homogeneous manifolds
Author(s):
Isaac
Pesenson
Journal:
Trans. Amer. Math. Soc.
352
(2000),
4257-4269.
MSC (2000):
Primary 43A85, 58G03;
Secondary 41A15
Posted:
April 21, 2000
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Abstract:
We consider a generalization of entire functions of spherical exponential type and Lagrangian splines on manifolds. An analog of the Paley-Wiener theorem is given. We also show that every spectral entire function on a manifold is uniquely determined by its values on some discrete sets of points. The main result of the paper is a formula for reconstruction of spectral entire functions from their values on discrete sets using Lagrangian splines.
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Additional Information:
Isaac
Pesenson
Affiliation:
Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
Email:
pesenson@math.temple.edu
DOI:
10.1090/S0002-9947-00-02592-7
PII:
S 0002-9947(00)02592-7
Keywords:
Shannon-Whittaker formula,
manifold,
Laplace-Beltrami operator,
spectral entire functions,
Lagrangian splines,
Sobolev spaces
Received by editor(s):
June 17, 1997
Received by editor(s) in revised form:
June 26, 1998
Posted:
April 21, 2000
Copyright of article:
Copyright
2000,
American Mathematical Society
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