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Shubin type Fourier integral operators and evolution equations
University of Turin, Italy.
Universität Hannover, Germany.
Linnaeus University, Faculty of Technology, Department of Mathematics.
2019 (English)In: Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, E-ISSN 1662-999XArticle in journal (Refereed) Epub ahead of print
Abstract [en]

We study the Cauchy problem for an evolution equation of Schrödinger type. The Hamiltonian is the Weyl quantization of a real homogeneous quadratic form with a pseudodifferential perturbation of negative order from Shubin’s class. We prove that the propagator is a Fourier integral operator of Shubin type of order zero. Using results for such operators and corresponding Lagrangian distributions, we study the propagator and the solution, and derive phase space estimates for them.

Place, publisher, year, edition, pages
Springer, 2019.
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics; Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-81571DOI: 10.1007/s11868-019-00288-0OAI: oai:DiVA.org:lnu-81571DiVA, id: diva2:1301405
Available from: 2019-04-01 Created: 2019-04-01 Last updated: 2019-08-28

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Wahlberg, Patrik

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