On the Schrödinger equation with potential in modulation spaces

Abstract

This work deals with Schrödinger equations with quadratic and sub-quadratic Hamiltonians perturbed by a potential. In particular we shall focus on bounded, but not necessarily smooth perturbations. We shall give a representation of such evolution as the composition of a metaplectic operator and a pseudodifferential operator having symbol in certain classes of modulation spaces. About propagation of singularities, we use a new notion of wave front set, which allows the expression of optimal results of propagation in our context. To support this claim, many comparisons with the existing literature are performed in this work.

25 pages

References in corpus (5)

• Generalized Metaplectic Operators and the Schrödinger Equation with a Potential in the Sjöstrand Class
• Schrödinger equations with rough Hamiltonians
• Semiclassical Singularity Propagation Property for Schrödinger Equations
• Estimates on modulation spaces for Schrödinger evolution operators with quadratic and sub-quadratic potentials
• Microlocal analysis of quasianalytic Gelfand-Shilov type ultradistributions

Cited by in corpus (2)

• Time-frequency analysis of the Dirac equation
• The nonlinear Schrödinger equations with harmonic potential in modulation spaces