Propagation of anisotropic Gabor singularities for Schrödinger type equations
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911808210599936 |
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| author | Cappiello, Marco Rodino, Luigi Wahlberg, Patrik |
| author_facet | Cappiello, Marco Rodino, Luigi Wahlberg, Patrik |
| contents | We show results on propagation of anisotropic Gabor wave front sets for solutions to a class of evolution equations of Schrödinger type. The Hamiltonian is assumed to have a real-valued principal symbol with the anisotropic homogeneity $a(λx, λ^σξ) = λ^{1+σ} a(x,ξ)$ for $λ> 0$ where $σ> 0$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_08010 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Propagation of anisotropic Gabor singularities for Schrödinger type equations Cappiello, Marco Rodino, Luigi Wahlberg, Patrik Analysis of PDEs 46F05, 46F12, 35A27, 47G30, 35S05, 35A18, 81S30, 58J47, 47D06 We show results on propagation of anisotropic Gabor wave front sets for solutions to a class of evolution equations of Schrödinger type. The Hamiltonian is assumed to have a real-valued principal symbol with the anisotropic homogeneity $a(λx, λ^σξ) = λ^{1+σ} a(x,ξ)$ for $λ> 0$ where $σ> 0$ 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. |
| title | Propagation of anisotropic Gabor singularities for Schrödinger type equations |
| topic | Analysis of PDEs 46F05, 46F12, 35A27, 47G30, 35S05, 35A18, 81S30, 58J47, 47D06 |
| url | https://arxiv.org/abs/2307.08010 |