Balian-Low phenomenon for subspace Gabor frames

    Authors

    J. P. Gabardo;D. G. Han

    Comments

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    Abbreviated Journal Title

    J. Math. Phys.

    Keywords

    WEYL-HEISENBERG FRAMES; LOW THEOREM; LATTICES; ALGEBRAS; SCHEMES; Physics, Mathematical

    Abstract

    In this work, the Balian-Low theorem is extended to Gabor (also called Weyl-Heisenberg) frames for subspaces and, more particularly, its relationship with the unique Gabor dual property for subspace Gabor frames is pointed out. To achieve this goal, the subspace Gabor frames which have a unique Gabor dual of type I (resp. type II) are defined and characterized in terms of the Zak transform for the rational parameter case. This characterization is then used to prove the Balian-Low theorem for subspace Gabor frames. Along the same line, the same characterization is used to prove a duality theorem for the unique Gabor dual property which is an analogue of the Ron and Shen duality theorem. (C) 2004 American Institute of Physics.

    Journal Title

    Journal of Mathematical Physics

    Volume

    45

    Issue/Number

    8

    Publication Date

    1-1-2004

    Document Type

    Article

    Language

    English

    First Page

    3362

    Last Page

    3378

    WOS Identifier

    WOS:000222802000022

    ISSN

    0022-2488

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