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On the Inverse to the Harmonic Oscillator
Univ Turin, Italy.
Univ Turin, Italy.
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0003-1921-8168
2015 (English)In: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 40, no 6, 1096-1118 p.Article in journal (Refereed) Published
Abstract [en]

Let b ( d ) be the Weyl symbol of the inverse to the harmonic oscillator on R- d . We prove that b ( d ) and its derivatives satisfy convenient bounds of Gevrey and Gelfand-Shilov type, and obtain explicit expressions for b ( d ). In the even-dimensional case we characterize b ( d ) in terms of elementary functions. In the analysis we use properties of radial symmetry and a combination of different techniques involving classical a priori estimates, commutator identities, power series and asymptotic expansions.

Place, publisher, year, edition, pages
2015. Vol. 40, no 6, 1096-1118 p.
Keyword [en]
46F05, 35S05, Secondary 33C10, Primary 35Q40, 30Gxx, Ultradistributions, Harmonic oscillator, Gelfand-Shilov estimates, Inverse
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-41390DOI: 10.1080/03605302.2015.1007145ISI: 000350824400004OAI: oai:DiVA.org:lnu-41390DiVA: diva2:798406
Available from: 2015-03-26 Created: 2015-03-26 Last updated: 2017-01-11Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
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  • de-DE
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  • nn-NO
  • nn-NB
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  • Other locale
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  • asciidoc
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