Title

When a characteristic function generates a Gabor frame

Authors

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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