Oversampling of wavelet frames for real dilations

Marcin Bownik, Jakob Lemvig

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    Abstract

    We generalize the Second Oversampling Theorem for wavelet frames and dual wavelet frames from the setting of integer dilations to real dilations. We also study the relationship between dilation matrix oversampling of semi-orthogonal Parseval wavelet frames and the additional shift invariance gain of the core subspace.
    Original languageEnglish
    JournalJournal of the London Mathematical Society
    Volume85
    Issue number3
    Pages (from-to)765-788
    ISSN0024-6107
    DOIs
    Publication statusPublished - 2012

    Keywords

    • Transversal constellation
    • Second Oversampling Theorem
    • Real dilations
    • Approximate dual lattice
    • Affine frames
    • Shift invariant subspaces
    • Wavelets
    • Approximate transversal
    • Lattice

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