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Mediterranean Journal of Mathematics

, Volume 2, Issue 4, pp 381–394 | Cite as

Localization Operators and Exponential Weights for Modulation Spaces

  • Elena Cordero
  • Stevan Pilipović
  • Luigi Rodino
  • Nenad Teofanov
Original Paper

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.

Mathematics Subject Classification (2000).

47G30 35S05 46F05 44A05 

Keywords.

Localization operator ultra-distributions Gelfand-Shilov type spaces modulation space Wigner distribution short-time Fourier transform Schatten class 

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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  • Elena Cordero
    • 1
  • Stevan Pilipović
    • 2
  • Luigi Rodino
    • 1
  • Nenad Teofanov
    • 2
  1. 1.Dipartimento of MatematicaUniversità of Torino Italy
  2. 2.Department of Mathematics and InformaticsUniv. of Novi Sad Serbia and Montenegro

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