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

    Authors

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

    Comments

    Authors: contact us about adding a copy of your work at [email protected]

    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

    Share

    COinS
     

    Accessibility Statement

    This item was created or digitized prior to April 24, 2027, or is a reproduction of legacy media created before that date. It is preserved in its original, unmodified state specifically for research, reference, or historical recordkeeping. In accordance with the ADA Title II Final Rule, the University Libraries provides accessible versions of archival materials upon request. To request an accommodation for this item, please submit an accessibility request form.