The existence of tight Gabor duals for Gabor frames and subspace Gabor frames

    Authors

    D. G. Han

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    Abstract

    Let K and L be two full-rank lattices in R(d). We give a complete characterization for all the Gabor frames that admit tight dual of the same type. The characterization is given in terms of the center-valued trace of the von Neumann algebra generated by the left regular projective unitary representations associated with the time-frequency lattice K x L. Two applications of this characterization were obtained: (i) We are able to prove that every Gabor frame has a tight dual if and only if the volume of K x L is less than or equal to 1/2. (ii) We are able to obtain sufficient or necessary conditions for the existence of tight Gabor pseudo-duals for subspace Gabor frames in various cases. In particular, we prove that every subspace Gabor frame has a tight Gabor pseudo-dual if either the volume v(K x L) < = 1/2 or v(K x L) > = 2. Moreover, if K = alpha Z(d), L = beta Z(d) with alpha beta = 1, then a subspace Gabor frame G(g, L, K) has a tight Gabor pseudo-dual only when G(g, L, K) itself is already tight. (C) 2008 Elsevier Inc. All rights reserved.

    Journal Title

    Journal of Functional Analysis

    Volume

    256

    Issue/Number

    1

    Publication Date

    1-1-2009

    Document Type

    Article

    First Page

    129

    Last Page

    148

    WOS Identifier

    WOS:000261748200003

    ISSN

    0022-1236

    Share

    COinS