Pointwise convergence of a class of non-orthogonal wavelet expansions

    Authors

    A. I. Zayed

    Abbreviated Journal Title

    Proc. Amer. Math. Soc.

    Keywords

    non-orthogonal wavelets; Shannon's wavelet; wavelet expansions; pointwise convergence; Mathematics, Applied; Mathematics

    Abstract

    Non-orthogonal wavelet expansions associated with a class of mother wavelets is considered. This class of wavelets comprises mother wavelets that are not necessarily integrable over the whole real line, such as Shannon's wavelet. The pointwise convergence of these wavelet expansions is investigated. It is shown that, unlike other wavelet expansions, the ones under consideration do not necessarily converge pointwise to the functions at points of continuity, unless a more stringent condition, such as bounded variation, is imposed.

    Journal Title

    Proceedings of the American Mathematical Society

    Volume

    128

    Issue/Number

    12

    Publication Date

    1-1-2000

    Document Type

    Article

    Language

    English

    First Page

    3629

    Last Page

    3637

    WOS Identifier

    WOS:000089527300024

    ISSN

    0002-9939

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