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Compactness Properties for Modulation Spaces
Univ Regensburg, Germany.
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0003-1921-8168
2019 (English)In: Complex Analysis and Operator Theory, ISSN 1661-8254, E-ISSN 1661-8262, Vol. 13, no 8, p. 3521-3548Article in journal (Refereed) Published
Abstract [en]

We prove that if omega(1) and omega(2) are moderate weights and B is a suitable (quasi-)Banach function space, then a necessary and sufficient condition for the embedding i : M(omega(1), B) -> M(omega(2), B) between two modulation spaces to be compact is that the quotient omega(2)/omega(1) vanishes at infinity. Moreoverwe show, that the boundedness of omega(2)/omega(1) is a necessary and sufficient condition for the previous embedding to be continuous.

Place, publisher, year, edition, pages
Springer, 2019. Vol. 13, no 8, p. 3521-3548
Keywords [en]
Gelfand-Shilov spaces, Distributions, Bargmann transform, Quasi-Banach spaces
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-90851DOI: 10.1007/s11785-019-00903-4ISI: 000503400100003Scopus ID: 2-s2.0-85062771057OAI: oai:DiVA.org:lnu-90851DiVA, id: diva2:1384769
Available from: 2020-01-10 Created: 2020-01-10 Last updated: 2020-12-14Bibliographically approved

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Toft, Joachim

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