Title

When A Characteristic Function Generates A Gabor Frame

Keywords

Frames; Gabor frame; Gabor system

Abstract

We investigate the characterization problem which asks for a classification of all the triples (a, b, c) such that the Gabor system {ei 2 m π b t χ[n a, c + n a) : m, n ∈ Z} is a frame for L2 (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. © 2007 Elsevier Inc. All rights reserved.

Publication Date

5-1-2008

Publication Title

Applied and Computational Harmonic Analysis

Volume

24

Issue

3

Number of Pages

290-309

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.acha.2007.06.005

Socpus ID

41349112706 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/41349112706

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