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The Range of Localization Operators and Lifting Theorems for Modulation and Bargmann-Fock Spaces
Linnaeus University, Faculty of Technology, Department of Mathematics. (Matematisk modellering, Center för avancerade studier)ORCID iD: 0000-0003-1921-8168
2013 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 365, no 8, 4475-4496 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2013. Vol. 365, no 8, 4475-4496 p.
National Category
Mathematical Analysis
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-18110DOI: 10.1090/S0002-9947-2013-05836-9ISI: 000326588800018Scopus ID: 2-s2.0-84877974786OAI: oai:DiVA.org:lnu-18110DiVA: diva2:512131
Projects
Matematisk modellering, Centrum för avancerade studier
Available from: 2012-03-26 Created: 2012-03-26 Last updated: 2017-05-08Bibliographically approved

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