Analytic Wave Front Set for Solutions to Schrödinger Equations II -- Long Range Perturbations
| dc.creator | Martinez, Andre' | |
| dc.creator | Nakamura, Shu | |
| dc.creator | Sordoni, Vania | |
| dc.date | 2008-07-31 | |
| dc.date.accessioned | 2026-07-07T09:53:57Z | |
| dc.date.available | 2026-07-07T09:53:57Z | |
| dc.description | This paper is a continuation of a paper by the authors: arXiv:0706.0415, where short range perturbations of the flat Euclidian metric where considered. Here, we generalize the results of the paper to long-range perturbations (in particular, we can allow potentials growing like $<x>^{2-\varepsilon}$ at infinity). More precisely, we construct a modified quantum free evolution $G_0(-s, hD_z)$ acting on Sjöstrand's spaces, and we characterize the analytic wave front set of the solution $e^{-itH}u_0$ of the Schrödinger equation, in terms of the semiclassical exponential decay of $G_0(-th^{-1}, hD_z)T u_0$, where $T$ stands for the Bargmann-transform. The result is valid for $t<0$ near the forward non trapping points, and for $t>0$ near the backward non trapping points. It is an extension of a paper by Nakamura (arXiv:math/0605742) to the analytic framework. | |
| dc.description | 34 pages | |
| dc.identifier | https://arxiv.org/abs/0807.4982 | |
| dc.identifier | http://arxiv.org/abs/0807.4982 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166138 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 35A21; 35J10; 35Q40 | |
| dc.title | Analytic Wave Front Set for Solutions to Schrödinger Equations II -- Long Range Perturbations | |
| dc.type | text |