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.

Shubin type Fourier integral operators and evolution equations / Cappiello, Marco; Schulz, René; Wahlberg, Patrik. - In: JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS. - ISSN 1662-9981. - 11:1(2020), pp. 119-139. [10.1007/s11868-019-00288-0]

Shubin type Fourier integral operators and evolution equations

Cappiello, Marco;Wahlberg, Patrik
2020

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2961110