The Balian-Low theorem for symplectic lattices in higher dimensions

    Authors

    K. Grochenig; D. G. Han; C. Heil;G. Kutyniok

    Abbreviated Journal Title

    Appl. Comput. Harmon. Anal.

    Keywords

    Balian-Low theorem; frames; Gabor systems; modulation spaces; symplectic; matrices; uncertainty principles; GABOR FRAMES; Mathematics, Applied; Physics, Mathematical

    Abstract

    The Balian-Low theorem expresses the fact that time-frequency concentration is incompatible with non-redundancy for Gabor systems that form orthonormal or Riesz bases for L-2(R). We extend the Balian-Low theorem for Riesz bases to higher dimensions, obtaining a weak form valid for all sets of time-frequency shifts which form a lattice in R-2d, and a strong form valid for symplectic lattices in R-2d. For the orthonormal basis case, we obtain a strong form valid for general non-lattice sets which are symmetric with respect to the origin. (C) 2002 Elsevier Science (USA). All rights reserved.

    Journal Title

    Applied and Computational Harmonic Analysis

    Volume

    13

    Issue/Number

    2

    Publication Date

    1-1-2002

    Document Type

    Article

    Language

    English

    First Page

    169

    Last Page

    176

    WOS Identifier

    WOS:000179970200006

    ISSN

    1063-5203

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