On the time-frequency representation of operators and generalized Gabor multiplier approximationsReportar como inadecuado




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1 NuHAG - Numerical Harmonic Analysis Group, Faculty of Mathematics 2 LATP - Laboratoire d-Analyse, Topologie, Probabilités

Abstract : Starting from a general operator representation in the time-frequency do- main, this paper addresses the problem of approximating linear operators by operators that are diagonal or band-diagonal with respect to Gabor frames. A characterization of operators that can be realized as Gabor multipliers is given and necessary conditions for the existence of Hilbert-Schmidt optimal Gabor multiplier approximations are discussed and an efficient method for the calculation of an operator-s best approximation by a Gabor multiplier is derived. The spreading function of Gabor multipliers yields new error estimates for these approximations. Generalizations multiple Gabor multipliers are introduced for better approximation of overspread operators. The Riesz property of the projection operators involved in generalized Gabor multipliers is characterized, and a method for obtaining an operator-s best approximation by a multiple Gabor multiplier is suggested. Finally, it is shown that in certain situations, generalized Gabor multipliers reduce to a finite sum of regular Gabor multipliers with adapted windows.

Keywords : Spreading function Twisted convolution Operator approximation Generalized Gabor multipliers





Autor: Monika Dörfler - Bruno Torrésani -

Fuente: https://hal.archives-ouvertes.fr/



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