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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A sampling theorem on homogeneous manifolds


Author: Isaac Pesenson
Journal: Trans. Amer. Math. Soc. 352 (2000), 4257-4269
MSC (2000): Primary 43A85, 58G03; Secondary 41A15
Published electronically: April 21, 2000
MathSciNet review: 1707201
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Abstract | References | Similar Articles | Additional Information

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: http://dx.doi.org/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
Published electronically: April 21, 2000
Article copyright: © Copyright 2000 American Mathematical Society