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Isomorphism properties of Toeplitz operators and pseudo-differential operators between modulation spaces

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Abstract

We investigate the lifting property of modulation spaces and construct explicit isomorphisms between them. For each weight function ω and suitable window function φ, the Toeplitz operator (or localization operator) Tp φ (ω) is an isomorphism from \(M_{({\omega _0})}^{p,q}\), onto \(M_{({\omega _0}/\omega )}^{p,q}\) for every p, q ∈ [1,∞] and arbitrary weight function ω 0. The methods involve the pseudo-differential calculus of Bony and Chemin and the Wiener algebra property of certain symbol classes of pseudo-differential Operators.

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Author notes

  1. Joachim Toft

    Present address: Department of Mathematics and Systems Engineering, Växjö University, Växjö, Sweden

Authors and Affiliations

  1. Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, A-1090, Vienna, Austria

    Karlheinz Gröchenig

  2. Department of Computer Science, Mathematics and Physics, Linnæus University, Växjö, Sweden

    Joachim Toft

Authors
  1. Karlheinz Gröchenig
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  2. Joachim Toft
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Corresponding author

Correspondence to Karlheinz Gröchenig.

Additional information

K.G. was supported by the Marie-Curie Excellence Grant. MEXT-CT-2004-517154

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Gröchenig, K., Toft, J. Isomorphism properties of Toeplitz operators and pseudo-differential operators between modulation spaces. JAMA 114, 255–283 (2011). https://doi.org/10.1007/s11854-011-0017-8

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  • DOI: https://doi.org/10.1007/s11854-011-0017-8

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