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Propagation of Gabor singularities for Schrödinger equations with quadratic Hamiltonians
Université de Rennes 1, France.
University of Turin, Italy;RUDN University, Russia.
Linnaeus University, Faculty of Technology, Department of Mathematics.
2018 (English)In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 291, no 1, p. 128-159Article in journal (Refereed) Published
Abstract [en]

We study propagation of the Gabor wave front set for a Schrödinger equation wit ha Hamiltonian that is the Weyl quantization of a quadratic form with nonnegativereal part. We point out that t he singular space associated with the quadratic formplays a crucial role for the understanding of this propagation. We show that the Gaborsingularities of the solution to the equation for positive times are always contained inthe singular space, and that t hey propagate in this set along the flow of the Hamiltonvector field associated with the imaginary part of the quadratic form. As an applicationwe obtain for the heat equation a sufficient condition on the Gabor wave front set of theinitial datum tempered distribution that implies regularization to Schwartz regularityfor positive times.

Place, publisher, year, edition, pages
Wiley-Blackwell, 2018. Vol. 291, no 1, p. 128-159
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-61660DOI: 10.1002/mana.201600410ISI: 000419960200010OAI: oai:DiVA.org:lnu-61660DiVA, id: diva2:1084146
Available from: 2017-03-23 Created: 2017-03-23 Last updated: 2018-02-08Bibliographically approved

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Wahlberg, Patrik

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