Title

Sampling in a Hilbert space

Authors

Authors

A. I. Zayed

Comments

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Abbreviated Journal Title

Proc. Amer. Math. Soc.

Keywords

Shannon's sampling theorem; interpolation and approximation in a Hilbert; space; frames and frame operators; Mathematics, Applied; Mathematics

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.

Journal Title

Proceedings of the American Mathematical Society

Volume

124

Issue/Number

12

Publication Date

1-1-1996

Document Type

Article

DOI Link

http://dx.doi.org/10.1090/s0002-9939-96-03526-5

Language

English

First Page

3767

Last Page

3776

WOS Identifier

WOS:A1996TG80100005

ISSN

0002-9939

Recommended Citation

"Sampling in a Hilbert space" (1996). Faculty Bibliography 1990s. 1814.
https://stars.library.ucf.edu/facultybib1990/1814