When a characteristic function generates a Gabor frame

    Authors

    Q. Gu;D. G. Han

    Comments

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    Abbreviated Journal Title

    Appl. Comput. Harmon. Anal.

    Keywords

    frames; Gabor system; Gabor frame; BARGMANN-FOCK SPACE; DENSITY THEOREMS; INTERPOLATION; EXPANSIONS; TRANSFORMS; Mathematics, Applied; Physics, Mathematical

    Abstract

    We investigate the characterization problem which asks for a classification of all the triples (a, b, c) such that the Gabor system {e(i2m pi bt) chi([na,c+na)): M, n is an element of Z} is a frame for L-2(R). We present a new approach to this problem. With the help of a set-valued mapping defined on certain union of intervals, we are able to provide a complete solution for the case of ab being a rational number. For the irrational case, we prove that the classification problem can also be completely settled if the union of some intervals obtained from the set-valued mapping becomes stabilized after finitely many times of iterations, which we conjecture is always true. (C) 2007 Elsevier Inc. All rights reserved.

    Journal Title

    Applied and Computational Harmonic Analysis

    Volume

    24

    Issue/Number

    3

    Publication Date

    1-1-2008

    Document Type

    Article

    Language

    English

    First Page

    290

    Last Page

    309

    WOS Identifier

    WOS:000255723400002

    ISSN

    1063-5203

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