Sampling in a Hilbert space

    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

    Language

    English

    First Page

    3767

    Last Page

    3776

    WOS Identifier

    WOS:A1996TG80100005

    ISSN

    0002-9939

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