Super-wavelets and deeomposable wavelet frames

    Authors

    Q. Gu;D. G. Han

    Comments

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    Abbreviated Journal Title

    J. Fourier Anal. Appl.

    Keywords

    wavelet; super-wavelet; decomposable and extendable Parseval wavelet; frames; Mathematics, Applied

    Abstract

    A wavelet frame is called decomposable whenever it is equivalent to a super-wavelet frame of length greater than one. Decomposable wavelet frames are closely related to some problems on super-wavelets. In this article we first obtain some necessary or sufficient conditions for decomposable Parseval wavelet frames. As an application of these conditions, we prove that for each n > 1 there exists a Parseval wavelet frame which is m-decomposable for any 1 < m < n, but not k-decomposable for any k > n. Moreover; there exists a super-wavelet whose components are non-decomposable. Similarly we also prove that for each n > 1, there exists a Parseval wavelet frame that can be extended to a super-wavelet of length m for any 1 < m < = n, but can not be extended to any super-wavelet of length k with k > n. The connection between decomposable Parseval wavelet frames and super-wavelets is investigated, and some necessary or sufficient conditions for extendable Parseval wavelet frames are given.

    Journal Title

    Journal of Fourier Analysis and Applications

    Volume

    11

    Issue/Number

    6

    Publication Date

    1-1-2005

    Document Type

    Article

    Language

    English

    First Page

    683

    Last Page

    696

    WOS Identifier

    WOS:000234544400005

    ISSN

    1069-5869

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