Title
Lattice Tiling And Density Conditions For Subspace Gabor Frames
Keywords
Frame; Gabor frame; Tiling; Translation and modulation operators
Abstract
The well known density theorem in time-frequency analysis establishes the connection between the existence of a Gabor frame G(g,A,B)={e2πi〈Bm,x〉g(x-An):m,n∈Zd} for L2(Rd) and the density of the time-frequency lattice AZd×BZd. This is also tightly related to lattice tiling and packing. In this paper we investigate the density theorem for Gabor systems in L2(S) with S being an AZd-periodic subset of Rd. We characterize the existence of a Gabor frame for L2(S) in terms of a condition that involves the Haar measure of the group generated by AZd and (Bt)-1Zd. This new characterization is used to recover the density theorem and several related known results in the literature. Additionally we apply this approach to obtain the density theorems for multi-windowed and super Gabor frames for L2(S). © 2013 Elsevier Inc.
Publication Date
10-1-2013
Publication Title
Journal of Functional Analysis
Volume
265
Issue
7
Number of Pages
1170-1189
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1016/j.jfa.2013.05.032
Copyright Status
Unknown
Socpus ID
84880137361 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84880137361
STARS Citation
Gabardo, Jean Pierre; Han, Deguang; and Li, Yun Zhang, "Lattice Tiling And Density Conditions For Subspace Gabor Frames" (2013). Scopus Export 2010-2014. 6283.
https://stars.library.ucf.edu/scopus2010/6283