Title

Lattice tiling and density conditions for subspace Gabor frames

Authors

Authors

J. P. Gabardo; D. G. Han;Y. Z. Li

Comments

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Abbreviated Journal Title

J. Funct. Anal.

Keywords

Frame; Gabor frame; Tiling; Translation and modulation operators; WEYL-HEISENBERG FRAMES; Mathematics

Abstract

The well known density theorem in time-frequency analysis establishes the connection between the existence of a Gabor frame G(g, A, B) = {e(2 pi i < Bm,x >) g(x - An): m, n is an element of Z(d)} for L-2(R-d) and the density of the time-frequency lattice AZ(d) x BZ(d). This is also tightly related to lattice tiling and packing. In this paper we investigate the density theorem for Gabor systems in L-2(S) with S being an AZ(d)-periodic subset of R-d. We characterize the existence of a Gabor frame for L-2(S) in terms of a condition that involves the Haar measure of the group generated by AZ(d) and (B-t)(-1)Z(d). 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 L-2(S). (C) 2013 Elsevier Inc. All rights reserved.

Journal Title

Journal of Functional Analysis

Volume

265

Issue/Number

7

Publication Date

1-1-2013

Document Type

Article

Language

English

First Page

1170

Last Page

1189

WOS Identifier

WOS:000322053200003

ISSN

0022-1236

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