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Generalized free time-dependent Schrödinger equation with initial data in Fourier Lebesgue spaces
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
2011 (English)In: Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, E-ISSN 1662-999X, Vol. 2, no 4, p. 543-556Article in journal (Refereed) Published
Abstract [en]

Consider the solution of the free time-dependent Schrödinger equation with initial data f. It is shown by Sjögren and Sjölin that there exists f in the Sobolev spaceHs (Rd ), s = d/2 such that tangential convergence can not be widened to convergence regions. The author obtained in a previous paper the corresponding results for a generalized version of the Schrödinger equation, where −Δx is replaced by an operator ϕ(D), with special conditions on ϕ. In this paper we show that similar results may be obtained for initial data in usual and mixed Fourier Lebesgue spaces. We also relax the conditions on ϕ.

Place, publisher, year, edition, pages
Basel: Birkhäuser Verlag, 2011. Vol. 2, no 4, p. 543-556
Keywords [en]
Generalized time-dependent Schrödinger equation, Non-tangential convergence, Fourier Lebesgue spaces
National Category
Mathematical Analysis
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-14059DOI: 10.1007/s11868-011-0041-6Scopus ID: 2-s2.0-84873834938OAI: oai:DiVA.org:lnu-14059DiVA, id: diva2:477833
Available from: 2012-01-13 Created: 2011-09-09 Last updated: 2017-12-08Bibliographically approved

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Johansson, Karoline

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  • en-US
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  • nn-NB
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  • Other locale
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