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The Bargmann transform on modulation and Gelfand-Shilov spaces, with applications to Toeplitz and pseudo-differential operators
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics. (Matematisk modellering, Center för avancerade studier)ORCID iD: 0000-0003-1921-8168
2012 (English)In: Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, E-ISSN 1662-999X, Vol. 3, no 2, p. 145-227Article in journal (Refereed) Published
Abstract [en]

We investigate mapping properties for the Bargmann transform on an extended family ofmodulation spaces whose weights and their reciprocals are allowed to grow faster than exponentials. We provethat this transform is isometric and bijective from modulation spacesto convenient Lebesgue spaces of analytic functions. We use this to prove that suchmodulation spaces fulfill most of the continuity properties which are valid for modulationspaces with moderate weights. Finally we use the results to establish continuity propertiesof Toeplitz and pseudo-differential operators on these modulation spaces, and onGelfand-Shilov spaces.

Place, publisher, year, edition, pages
Birkhäuser, Springer , 2012. Vol. 3, no 2, p. 145-227
Keywords [en]
Bijectivity properties, Analytic, Short-time Fourier transform, Gelfand-Shilov spaces, Berezin-Toeplitz operators
National Category
Mathematical Analysis
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-15844DOI: 10.1007/s11868-011-0044-3Scopus ID: 2-s2.0-84873051355OAI: oai:DiVA.org:lnu-15844DiVA, id: diva2:457837
Projects
Matematik och modelleringCenter för avancerade studierAvailable from: 2011-11-20 Created: 2011-11-20 Last updated: 2017-12-08Bibliographically approved

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Toft, Joachim

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CiteExportLink to record
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  • apa
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
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Output format
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