Riesz sequences of translates and generalized duals with support on [0,1]

Ole Christensen, H.O. Kim, R.Y. Kim, J.K. Lim

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    If the integer translates of a function phi with compact support generate a frame for a subspace W of L-2(R), then it is automatically a Riesz basis for W, and there exists a unique dual Riesz basis belonging to W. Considerable freedom can be obtained by considering oblique duals, i.e., duals not necessarily belonging to W. Extending work by Ben-Artzi and Ron, we characterize the existence of oblique duals generated by a function with support on an interval of length one. If such a generator exists, we show that it can be chosen with desired smoothness. Regardless whether phi is polynomial or not, the same condition implies that a polynomial dual supported on an interval of length one exists.
    Original languageEnglish
    JournalJournal of Geometric Analysis
    Volume16
    Issue number4
    Pages (from-to)585-596
    ISSN1050-6926
    Publication statusPublished - 2006

    Keywords

    • short support
    • dual frame
    • frames of translates
    • dual generator

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