Tight frame approximation for multi-frames and super-frames

    Authors

    D. G. Han

    Comments

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    Abbreviated Journal Title

    J. Approx. Theory

    Keywords

    frames; projective unitary systems; multi-fraines and super-frames; approximation; approximation; Gabor frames; shift-invariant subspaces; WEYL-HEISENBERG FRAMES; GABOR FRAMES; BASES; Mathematics

    Abstract

    We consider a generator Phi = (phi(1),...,phi(N)) for either a multi-frame or a super-frame generated under the action of a projective unitary representation for a discrete countable group. Examples of such frames include Gabor multi-frames, Gabor super-frames and frames for shift-invariant subspaces. We show that there exists a unique normalized tight multi-frame (resp. super-frame) generator Psi = (psi(1),..,psi(N)) such that Sigma(j=1)(N)\\phi(J) - psi(j)\\(2) less than or equal to Sigma(j=1)(N)\\phi(j) - psi(j)\\(2) holds for all the normalized tight multi-frame (resp. super-frame) generators eta = (eta(1),...,eta(N)). We also investigate the similar problems for dual frames and discuss a few applications to Gabor frames and some other frames. (C) 2004 Elsevier Inc. All rights reserved.

    Journal Title

    Journal of Approximation Theory

    Volume

    129

    Issue/Number

    1

    Publication Date

    1-1-2004

    Document Type

    Article

    Language

    English

    First Page

    78

    Last Page

    93

    WOS Identifier

    WOS:000222712600004

    ISSN

    0021-9045

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