Propagation of Gabor singularities for Schrödinger equations with quadratic Hamiltonians

We study propagation of the Gabor wave front set for a Schrödinger equation with a Hamiltonian that is the Weyl quantization of a quadratic form with nonnegative real part. We point out that the singular space associated with the quadratic form plays a crucial role for the understanding of this propagation. We show that the Gabor singularities of the solution to the equation for positive times are always contained in the singular space, and that they propagate in this set along the flow of the Hamilton vector field associated with the imaginary part of the quadratic form. As an application we obtain for the heat equation a sufficient condition on the Gabor wave front set of the initial datum tempered distribution that implies regularization to Schwartz regularity for positive times. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Authors
Pravda-Starov K.1 , Rodino L. 2, 3 , Wahlberg P.4
Publisher
Wiley-VCH Verlag
Number of issue
1
Language
English
Pages
128-159
Status
Published
Volume
291
Year
2018
Organizations
  • 1 IRMAR, CNRS UMR 6625, Université de Rennes 1, Campus de Beaulieu, 263 avenue du Général Leclerc, CS 74205, Rennes cedex, 35042, France
  • 2 Department of Mathematics, University of Turin, Via Carlo Alberto 10, Torino (TO), 10123, Italy
  • 3 RUDN University, 6 Miklukho-Maklay St, Moscow, 117198, Russian Federation
  • 4 Department of Mathematics, Linnæus University, Växjö, SE–35195, Sweden
Keywords
35A18; 35A21; 35Q40; 35Q79; 35S10; Gabor wave front set; heat equation; propagation of singularities; Schrödinger equation; singular space
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/7328/
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