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

DOI:
https://doi.org/10.1090/S0002-9947-00-02592-7

Published electronically:
April 21, 2000

MathSciNet review:
1707201

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-00-02592-7

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