Sampling in a Hilbert space

Author:
Ahmed I. Zayed

Journal:
Proc. Amer. Math. Soc. **124** (1996), 3767-3776

MSC (1991):
Primary 41A05, 41A35; Secondary 47A58

DOI:
https://doi.org/10.1090/S0002-9939-96-03526-5

MathSciNet review:
1343731

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Abstract | References | Similar Articles | Additional Information

Abstract: An analog of the Whittaker-Shannon-Kotel'nikov sampling theorem is derived for functions with values in a separable Hilbert space. The proof uses the concept of frames and frame operators in a Hilbert space. One of the consequences of this theorem is that it allows us to derive sampling theorems associated with boundary-value problems and some homogeneous integral equations, which in turn gives us a generalization of another sampling theorem by Kramer.

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Additional Information

**Ahmed I. Zayed**

Affiliation:
Department of Mathematics, University of Central Florida, Orlando, Florida 32816

Email:
fdzayed@ucf1vm.cc.ucf.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03526-5

Keywords:
Shannon's sampling theorem,
interpolation and approximation in a Hilbert space,
frames and frame operators

Received by editor(s):
May 30, 1994

Received by editor(s) in revised form:
June 5, 1995

Communicated by:
J. Marshall Ash

Article copyright:
© Copyright 1996
American Mathematical Society