http://dx.doi.org/10.1006/jmaa.1994.1352

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Title

A Sampling Theorem For Signals Band-Limited To A General Domain In Several Dimensions

Authors

Authors

A. I. Zayed

Comments

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Abbreviated Journal Title

J. Math. Anal. Appl.

Keywords

STURM-LIOUVILLE PROBLEMS; LAGRANGE INTERPOLATION; Mathematics, Applied; Mathematics

Abstract

Sampling series expansions for functions (signals) that are bandlimited to N-dimensional rectangles (N greater-than-or-equal-to 1) have been studied extensively; however, if a function is bandlimited to a general region in R(N), not much is known about its sampling series expansion. In this paper, we derive a sampling theorem for functions that are bandlimited (in the sense of Kramer) to finite regions with smooth boundaries in R(N). The sampling series expansions obtained for these functions are Lagrange-type interpolation series. Our technique utilizes Green's function of the region involved. As an application of our sampling theorem, we obtain a new method for summing infinite series in several variables. (C) 1994 Academic Press, Inc.

Journal Title

Journal of Mathematical Analysis and Applications

Volume

187

Issue/Number

1

Publication Date

1-1-1995

Document Type

Article

Language

English

First Page

196

Last Page

211

WOS Identifier

WOS:A1994PL38300012

ISSN

0022-247X

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