- Title
- Vector-valued modulation spaces and localization operators with operator-valued symbols
- Creator
- Wahlberg, Patrik
- Relation
- Integral Equations and Operator Theory Vol. 59, Issue 1, p. 99-128
- Publisher Link
- http://dx.doi.org/10.1007/s00020-007-1504-2
- Publisher
- Birkhaeuser Verlag AG
- Resource Type
- journal article
- Date
- 2007
- Description
- 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 Lp,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.
- Subject
- time-frequency analysis; vector-valued modulation spaces; localization operators; pseudodifferential operators
- Identifier
- http://hdl.handle.net/1959.13/805841
- Identifier
- uon:6921
- Identifier
- ISSN:0378-620X
- Language
- eng
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