The semiclassical resolvent and the propagator for nontrapping scattering metrics
| dc.creator | Hassell, Andrew | |
| dc.creator | Wunsch, Jared | |
| dc.date | 2006-06-23 | |
| dc.date.accessioned | 2026-07-07T07:17:38Z | |
| dc.date.available | 2026-07-07T07:17:38Z | |
| dc.description | Consider a compact manifold with boundary $M$ with a scattering metric $g$ or, equivalently, an asymptotically conic manifold $(M^\circ, g)$. (Euclidean $\mathbb{R}^n$, with a compactly supported metric perturbation, is an example of such a space.) Let $Δ$ be the positive Laplacian on $(M,g)$, and $V$ a smooth potential on $M$ which decays to second order at infinity. In this paper we construct the kernel of the operator $(h^2 Δ+ V - (λ_0 \pm i0)^2)^{-1}$, at a nontrapping energy $λ_0 > 0$, uniformly for $h \in (0, h_0)$, $h_0 > 0$ small, within a class of Legendre distributions on manifolds with codimension three corners. Using this we construct the kernel of the propagator, $e^{-it(Δ/2 + V)}$, $t \in (0, t_0)$ as a quadratic Legendre distribution. We also determine the global semiclassical structure of the spectral projector, Poisson operator and scattering matrix. | |
| dc.identifier | https://arxiv.org/abs/math/0606606 | |
| dc.identifier | http://arxiv.org/abs/math/0606606 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114008 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Spectral Theory | |
| dc.subject | 35P20, 35P25, 58J40, 81U05, 81Q20 | |
| dc.title | The semiclassical resolvent and the propagator for nontrapping scattering metrics | |
| dc.type | text |