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Proceedings of the American Mathematical Society

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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
MathSciNet review: 1343731
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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

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