Sampling expansions for functions having values in a Banach space

    Authors

    D. G. Han;A. I. Zayed

    Comments

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    Abbreviated Journal Title

    Proc. Amer. Math. Soc.

    Keywords

    framing models; Banach spaces; atomic decomposition; interpolation; the; Whittaker-Shannon-Kotel'nikov sampling theorem; wavelet basis; INTEGRABLE GROUP-REPRESENTATIONS; ATOMIC DECOMPOSITIONS; FRAMES; Mathematics, Applied; Mathematics

    Abstract

    A sampling expansion for vector-valued functions having values in a Banach space, together with an inversion formula, is derived. The proof uses the concept of framing models of Banach spaces that generalizes the notion of frames in Hilbert spaces. Two examples illustrating the results are given, one involving functions having values in L-p[-pi, pi], 1 < p < = 2, and the second involving functions having values in L-p(R) for 1 < p < 8.

    Journal Title

    Proceedings of the American Mathematical Society

    Volume

    133

    Issue/Number

    12

    Publication Date

    1-1-2005

    Document Type

    Article

    Language

    English

    First Page

    3597

    Last Page

    3607

    WOS Identifier

    WOS:000231358100019

    ISSN

    0002-9939

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