Title
The Existence Of Tight Gabor Duals For Gabor Frames And Subspace Gabor Frames
Keywords
Frame representations; Frames; Gabor frames; Lattice tiling; Parseval duals; Pseudo-duals; Subspace Gabor frame
Abstract
Let K and L be two full-rank lattices in Rd. 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 × 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 × L is less than or equal to frac(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 × L) ≤ frac(1, 2) or v (K × L) ≥ 2. Moreover, if K = α Zd, L = β Zd with α β = 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. © 2008 Elsevier Inc. All rights reserved.
Publication Date
1-1-2009
Publication Title
Journal of Functional Analysis
Volume
256
Issue
1
Number of Pages
129-148
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1016/j.jfa.2008.10.015
Copyright Status
Unknown
Socpus ID
55649092269 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/55649092269
STARS Citation
Han, Deguang, "The Existence Of Tight Gabor Duals For Gabor Frames And Subspace Gabor Frames" (2009). Scopus Export 2000s. 12505.
https://stars.library.ucf.edu/scopus2000/12505