Semiclassical resolvent estimates in chaotic scattering - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Applied Mathematics Research eXpress Année : 2009

Semiclassical resolvent estimates in chaotic scattering

Résumé

We prove resolvent estimates for semiclassical operators such as $-h^2 \Delta+V(x)$ in scattering situations. Provided the set of trapped classical trajectories supports a chaotic flow and is sufficiently filamentary, the analytic continuation of the resolvent is bounded by $h^{-M}$ in a strip whose width is determined by a certain topological pressure associated with the classical flow. This polynomial estimate has applications to local smoothing in Schrödinger propagation and to energy decay of solutions to wave equations.
Fichier principal
Vignette du fichier
noz7.pdf (194.17 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00376771 , version 1 (20-04-2009)
hal-00376771 , version 2 (22-04-2009)
hal-00376771 , version 3 (10-09-2009)
hal-00376771 , version 4 (11-09-2009)

Identifiants

Citer

Stéphane Nonnenmacher, Maciej Zworski. Semiclassical resolvent estimates in chaotic scattering. Applied Mathematics Research eXpress, 2009, 2009, abp003. ⟨10.1093/amrx/abp003⟩. ⟨hal-00376771v4⟩
133 Consultations
139 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More