Lattice tiling and density conditions for subspace Gabor frames

    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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