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Images of function and distribution spaces under the Bargmann transform
Linnaeus University, Faculty of Technology, Department of Mathematics. (Matematisk modellering, Center för avancerade studier, ICMM)ORCID iD: 0000-0003-1921-8168
2017 (English)In: Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, E-ISSN 1662-999X, Vol. 8, no 1, 83-139 p.Article in journal (Refereed) Published
Abstract [en]

Weconsiderabroadfamilyoftestfunctionspacesandtheirdual(distribu- tion) spaces. The family includes Gelfand–Shilov spaces, and a family of test function spaces introduced by Pilipovic ́. We deduce different characterizations of such spaces, especially under the Bargmann transform and the Short-time Fourier transform. The family also include a test function space, whose dual space is mapped by the Bargmann transform bijectively to the set of entire functions. 

Place, publisher, year, edition, pages
Springer, 2017. Vol. 8, no 1, 83-139 p.
Keyword [en]
Gelfand–Shilov estimates, Pilipovic ́ spaces, Ultradistributions, Bargmann transform
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-61868DOI: 10.1007/s11868-016-0165-9ISI: 000394537800005OAI: oai:DiVA.org:lnu-61868DiVA: diva2:1084980
Projects
Matematisk modellering, ICMM
Available from: 2017-03-27 Created: 2017-03-27 Last updated: 2017-05-23Bibliographically approved

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