Open this publication in new window or tab >>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
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-61660 (URN)10.1002/mana.201600410 (DOI)000419960200010 ()2-s2.0-85018604578 (Scopus ID)
2017-03-232017-03-232019-08-29Bibliographically approved