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When a characteristic function generates a Gabor frame
Authors:Qing Gu  Deguang Han  
Affiliation:aDepartment of Mathematics, East China Normal University, Shanghai 200062, PR China;bDepartment of Mathematics, University of Central Florida, P.O. Box 161364, Orlando, FL 32816, USA
Abstract:We investigate the characterization problem which asks for a classification of all the triples (a,b,c) such that the Gabor system View the MathML source is a frame for View the MathML source. 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.
Keywords:Frames   Gabor system   Gabor frame
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