Shubin type Fourier integral operators and evolution equations View Full Text


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Article Info

DATE

2019-03-02

AUTHORS

Marco Cappiello, René Schulz, Patrik Wahlberg

ABSTRACT

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. More... »

PAGES

1-21

References to SciGraph publications

  • 2016-03. Microlocal properties of Shubin pseudodifferential and localization operators in JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS
  • 2014-04. The Gabor wave front set in MONATSHEFTE FÜR MATHEMATIK
  • 1991. Quadratic hyperbolic operators in MICROLOCAL ANALYSIS AND APPLICATIONS
  • 1995-05. Symplectic classification of quadratic forms, and general Mehler formulas in MATHEMATISCHE ZEITSCHRIFT
  • 2015-08. Integral Representations for the Class of Generalized Metaplectic Operators in JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
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    http://scigraph.springernature.com/pub.10.1007/s11868-019-00288-0

    DOI

    http://dx.doi.org/10.1007/s11868-019-00288-0

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