The range of localization operators and lifting theorems for modulation and Bargmann-Fock spaces
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Abstract:
We study the range of time-frequency localization operators acting on modulation spaces and prove a lifting theorem. As an application we also characterize the range of Gabor multipliers, and, in the realm of complex analysis, we characterize the range of certain Toeplitz operators on weighted Bargmann-Fock spaces. The main tools are the construction of canonical isomorphisms between modulation spaces of Hilbert-type and a refined version of the spectral invariance of pseudodifferential operators. On the technical level we prove a new class of inequalities for weighted gamma functions.References
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Additional Information
- Karlheinz Gröchenig
- Affiliation: Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, A-1090 Vienna, Austria
- Email: karlheinz.groechenig@univie.ac.at
- Joachim Toft
- Affiliation: Department of Computer Science, Physics and Mathematics, Linnæus University, Växjö, Sweden
- Email: joachim.toft@lnu.se
- Received by editor(s): October 3, 2011
- Received by editor(s) in revised form: March 22, 2012
- Published electronically: January 4, 2013
- Additional Notes: The first author was supported in part by the project P2276-N13 of the Austrian Science Fund (FWF)
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 4475-4496
- MSC (2010): Primary 46B03, 42B35, 47B35
- DOI: https://doi.org/10.1090/S0002-9947-2013-05836-9
- MathSciNet review: 3055702