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Vector-valued modulation spaces and localization operators with operator-valued symbols
The University of Newcastle.
2007 (English)In: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 59, no 1, 99-128 p.Article in journal (Refereed) Published
Abstract [en]

We study the short-time Fourier transformation, modulation spaces, Gabor representations and time-frequency localization operators, for functions and tempered distributions that have as range space a Banach or a Hilbert space. In the Banach space case the theory of modulation spaces contains some modifications of the scalar-valued theory, depending on the Banach space. In the Hilbert space case the modulation spaces have properties similar to the scalar-valued case and the Gabor frame theory essentially works. For localization operators in this context symbols are operator-valued. We generalize two results from the scalar-valued theory on continuity on certain modulation spaces when the symbol belongs to an L p,q space and M , respectively. The first result is true for any Banach space as range space, and the second result is true for any Hilbert space as range space.

Place, publisher, year, edition, pages
Basel: Birkhäuser Verlag, 2007. Vol. 59, no 1, 99-128 p.
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-27587DOI: 10.1007/s00020-007-1504-2OAI: oai:DiVA.org:lnu-27587DiVA: diva2:637389
Available from: 2013-07-17 Created: 2013-07-17 Last updated: 2013-08-16Bibliographically approved

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Wahlberg, Patrik
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CiteExportLink to record
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  • apa
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