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

Socpus ID

84880137361 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84880137361

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