Title

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

Authors

Authors

D. G. Han

Comments

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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

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