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On Toeplitz localization operators

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Abstract

We present a unified approach to study properties of Toeplitz localization operators based on the Calderón and Gabor reproducing formula. We show that these operators with functional symbols on a plane domain may be viewed as certain pseudo-differential operators (with symbols on a line, or certain compound symbols).

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References

  1. Bargmann V.: On a Hilbert space of analytic functions and an associated integral transform, Part I. Comm. Pure Appl. Math. 14, 187–214 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  2. Berezin F.A.: Method of Second Quantisation. Nauka, Moscow (1988)

    Google Scholar 

  3. Cordes H.O.: Pseudo-differential operators on a half-line. J. Math. Mech. 18, 893–908 (1969)

    MathSciNet  MATH  Google Scholar 

  4. Hutník O.: On Toeplitz-type operators related to wavelets. Integr. Equ. Oper. Theory 63, 29–46 (2009)

    Article  MATH  Google Scholar 

  5. Hutníková M., Hutník O.: An alternative description of Gabor spaces and Gabor-Toeplitz operators. Rep. Math. Phys. 66, 237–250 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Karlovich Yu.I.: Pseudodifferential operators with compound non-regular symbols. Math. Nachr. 280, 1128–1144 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Quiroga-Barranco R., Vasilevski N.L.: Commutative C*-algebras of Toeplitz operators on the unit ball, I. Bargmann-type transforms and spectral representations of Toeplitz operators. Integr. Equ. Oper. Theory 59, 379–419 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. N. L. Vasilevski, Commutative Algebras of Toeplitz Operators on the Bergman Space, Operator Theory: Advances and Applications 185 Birkhäuser, Basel, 2008.

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Authors and Affiliations

  1. Departamento de Matemáticas, CINVESTAV del IPN, Apartado Postal 14-740, 07000, México, D.F., México

    Ondrej Hutník

  2. Institute of Mathematics, Faculty of Science, P. J. Šafárik University in Košice, Jesenná 5, SK 040 01, Košice, Slovakia

    Ondrej Hutník

  3. Department of Physics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Park Komenského 2, SK 042 00, Košice, Slovakia

    Mária Hutníková

Authors
  1. Ondrej Hutník
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  2. Mária Hutníková
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Correspondence to Ondrej Hutník.

Additional information

This paper was supported by research project VVGS 45/10-11.

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Hutník, O., Hutníková, M. On Toeplitz localization operators. Arch. Math. 97, 333–344 (2011). https://doi.org/10.1007/s00013-011-0307-5

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  • DOI: https://doi.org/10.1007/s00013-011-0307-5

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