Pairs of oblique duals in spaces of periodic functions

Ole Christensen, Say Song Goh

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    We construct non-tight frames in finite-dimensional spaces consisting of periodic functions. In order for these frames to be useful in practice one needs to calculate a dual frame; while the canonical dual frame might be cumbersome to work with, the setup presented here enables us to obtain explicit constructions of some particularly convenient oblique duals. We also provide explicit oblique duals belonging to prescribed spaces different from the space where we obtain the expansion. In particular this leads to oblique duals that are trigonometric polynomials.
    Original languageEnglish
    JournalAdvances in Computational Mathematics
    Volume32
    Issue number3
    Pages (from-to)353-379
    ISSN1019-7168
    DOIs
    Publication statusPublished - 2010

    Keywords

    • Periodic frames
    • Oblique dual generators
    • Polyphase splines
    • Mixed Gramians

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