Frames and their associated H-F(p)-subspaces

    Authors

    D. G. Han; P. T. Li;W. S. Tang

    Comments

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    Abbreviated Journal Title

    Adv. Comput. Math.

    Keywords

    Frames; Riesz bases; Reconstruction; Dilation; LOCALIZATION; OPERATOR; OVERCOMPLETENESS; DENSITY; SYSTEMS; SPACES; Mathematics, Applied

    Abstract

    Given a frame F = {f(j)} for a separable Hilbert space H, we introduce the linear subspace H-F(p) of H consisting of elements whose frame coefficient sequences belong to the l(p)-space, where 1 < = p < 2. Our focus is on the general theory of these spaces, and we investigate different aspects of these spaces in relation to reconstructions, p-frames, realizations and dilations. In particular we show that for closed linear subspaces of H, only finite dimensional ones can be realized as H-F(p)-spaces for some frame F. We also prove that with a mild decay condition on the frame F the frame expansion of any element in H-F(p) converges in both the Hilbert space norm and the parallel to . parallel to(F, p-) norm which is induced by the l(p)-norm.

    Journal Title

    Advances in Computational Mathematics

    Volume

    34

    Issue/Number

    2

    Publication Date

    1-1-2011

    Document Type

    Article

    Language

    English

    First Page

    185

    Last Page

    200

    WOS Identifier

    WOS:000286189000003

    ISSN

    1019-7168

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