Title

Sampling with a string

Authors

Authors

A. Boumenir;A. I. Zayed

Comments

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Abbreviated Journal Title

J. Fourier Anal. Appl.

Keywords

Whittaker-Shannon's sampling theorem; Kramer's sampling theorem; Lagrange interpolation; string theory; Sturm-Liouville theory; STURM-LIOUVILLE PROBLEMS; LAGRANGE INTERPOLATION; COMPUTING EIGENVALUES; THEOREM; Mathematics, Applied

Abstract

Kramer's sampling theorem forms a bridge between the Whittaker-ShannonKotel'nikov sampling theorem and boundary-value problems. It has been shown that sampling expansions associated with Sturm-Liouville boundary-value problems are Lagrange-type sampling series, i.e., Lagrange series with infinitely many terms converging to entire functions. String theory as developed by Feller, Kac, and Krein, is a generalization of the Sturm-Liouville theory. We investigate sampling series associated with strings and compare them with those associated with Sturm-Liouville problems. We show that unlike sampling series associated with Sturm-Liouville problems, those associated with strings include not only Lagrange-type sampling series, but also Lagrange polynomial interpolation.

Journal Title

Journal of Fourier Analysis and Applications

Volume

8

Issue/Number

3

Publication Date

1-1-2002

Document Type

Article

Language

English

First Page

211

Last Page

231

WOS Identifier

WOS:000176113400001

ISSN

1069-5869

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