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Mixed-State Localization Operators: Cohen’s Class and Trace Class Operators

  • Franz LuefEmail author
  • Eirik Skrettingland
Article

Abstract

We study mixed-state localization operators from the perspective of Werner’s operator convolutions which allows us to extend known results from the rank-one case to trace class operators. The idea of localizing a signal to a domain in phase space is approached from various directions such as bounds on the spreading function, probability densities associated to mixed-state localization operators, positive operator valued measures, positive correspondence rules and variants of Tauberian theorems for operator translates. Our results include a rigorous treatment of multiwindow-STFT filters and a characterization of mixed-state localization operators as positive correspondence rules. Furthermore we provide a description of the Cohen class in terms of Werner’s convolution of operators and deduce consequences on positive Cohen class distributions, an uncertainty principle, uniqueness and phase retrieval for general elements of Cohen’s class.

Keywords

Localization operators Cohen class Uncertainty principle Phase retrieval Positive operator valued measures 

Mathematics Subject Classification

47G30 35S05 46E35 47B10 

Notes

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Authors and Affiliations

  1. 1.Department of MathematicsNTNU Norwegian University of Science and TechnologyTrondheimNorway

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