Back to Search
Start Over
Propagation of anisotropic Gabor singularities for Schr\'odinger type equations
- Publication Year :
- 2023
-
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.<br />Comment: 40 pages
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2307.08010
- Document Type :
- Working Paper