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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.
2017 (English)In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616Article in journal (Refereed) Epub ahead of print
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
2017.
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-61660DOI: 10.1002/mana.201600410OAI: oai:DiVA.org:lnu-61660DiVA: diva2:1084146
Available from: 2017-03-23 Created: 2017-03-23 Last updated: 2017-09-18

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CiteExportLink to record
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  • apa
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