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Propagation of exponential phase space singularities for Schrödinger equations with quadratic Hamiltonians
University of Turin, Italy.
Linnaeus University, Faculty of Technology, Department of Mathematics.
2017 (English)In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 23, no 3, 530-571 p.Article in journal (Refereed) Published
Abstract [en]

We study propagation of phase space singularities for the initial value Cauchy problem for a class of Schrödinger equations. The Hamiltonian is the Weyl quantization of a quadratic form whose real part is non-negative. The equations are studied in the framework of projective Gelfand–Shilov spaces and their distribution duals. The corresponding notion of singularities is called the Gelfand–Shilov wave front set and means the lack of exponential decay in open cones in phase space. Our main result shows that the propagation is determined by the singular space of the quadratic form, just as in the framework of the Schwartz space, where the notion of singularity is the Gabor wave front set.

Place, publisher, year, edition, pages
Springer, 2017. Vol. 23, no 3, 530-571 p.
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-51970DOI: 10.1007/s00041-016-9478-6ISI: 000401411900002OAI: oai:DiVA.org:lnu-51970DiVA: diva2:917849
Available from: 2016-04-08 Created: 2016-04-08 Last updated: 2017-07-18Bibliographically approved

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