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Localization Operators and Exponential Weights for Modulation Spaces
Authors:Elena Cordero  Stevan Pilipović  Luigi Rodino  Nenad Teofanov
Institution:(1) Dipartimento of Matematica, Università of Torino, , Italy;(2) Department of Mathematics and Informatics, Univ. of Novi Sad, , Serbia and Montenegro
Abstract:We study localization operators within the framework of ultradistributions. More precisely, given a symbol a and two windows φ1, φ2, we investigate the multilinear mapping from $$\left( {a,\varphi _1 ,\varphi _2 } \right) \in \,\mathcal{S}^{(1)\prime } (\mathbb{R}^{2d} ) \times \mathcal{S}^{(1)} (\mathbb{R}^d ) \times \mathcal{S}^{(1)} (\mathbb{R}^d )$$ to the localization operator $$A_a^{\varphi _1 ,\varphi _2 } .$$ Results are formulated in terms of modulation spaces with weights which may have exponential growth. We give sufficient and necessary conditions for $$A_a^{\varphi _1 ,\varphi _2 } $$ a to be bounded or to belong to a Schatten class. As an application, we study symbols defined by ultra-distributions with compact support, that give trace class localization operators.
Keywords:47G30  35S05  46F05  44A05
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