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arXiv · 2307.08010

Propagation of anisotropic Gabor singularities for Schr\"odinger type equations

Marco Cappiello·Luigi Rodino·Patrik Wahlberg
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Abstract

We show results on propagation of anisotropic Gabor wave front sets for solutions to a class of evolution equations of Schr\"odinger type. The Hamiltonian is assumed to have a real-valued principal symbol with the anisotropic homogeneity $a(\lambda x, \lambda^\sigma \xi) = \lambda^{1+\sigma} a(x,\xi)$ for $\lambda > 0$ where $\sigma > 0$ is a rational anisotropy parameter. We prove that the propagator is continuous on anisotropic Shubin--Sobolev spaces. The main result says that the propagation of the anisotropic Gabor wave front set follows the Hamilton flow of the principal symbol.

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Marco Cappiello, Luigi Rodino, Patrik Wahlberg. 2023-07-16. Propagation of anisotropic Gabor singularities for Schr\"odinger type equations. https://arxiv.org/abs/2307.08010

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