Structure of the Semi-Classical Amplitude for General Scattering Relations
| dc.creator | Alexandrova, Ivana | |
| dc.date | 2004-07-28 | |
| dc.date.accessioned | 2026-07-07T05:10:48Z | |
| dc.date.available | 2026-07-07T05:10:48Z | |
| dc.description | We consider scattering by general compactly supported semi-classical perturbations of the Euclidean Laplace-Beltrami operator. We show that if the suitably cut-off resolvent of the Hamiltonian quantizes a Lagrangian relation on the product cotangent bundle, the scattering amplitude quantizes the natural scattering relation. In the case when the resolvent is tempered, which is true under some non-resonance assumptions, and when we work microlocally near a non-trapped ray, our result implies that the scattering amplitude defines a semiclassical Fourier integral operator associated to the scattering relation in a neighborhood of that ray. Compared to previous work we allow this relation to have more general geometric structure. | |
| dc.description | 29 pages; 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0407502 | |
| dc.identifier | http://arxiv.org/abs/math/0407502 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72046 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35P25; 35S30 | |
| dc.title | Structure of the Semi-Classical Amplitude for General Scattering Relations | |
| dc.type | text |