Sampling with a string

    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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