HIGH FREQUENCY RESOLVENT ESTIMATES FOR THE MAGNETIC LAPLACIAN ON NON COMPACT MANIFOLDS
Résumé
We consider the Schrödinger operator with a magnetic perturbation on non compact manifolds with infinite volume. We prove optimal estimates for the resolvent operator at high frequencies in Besov-type spaces. In the general trapping case we obtain the usual exponential blow-up, while when the resolvent is localised on the manifold end, away from possible trapped trajectories, we obtain the optimal bound by the inverse square root of the spectral parameter.
| Origine | Fichiers produits par l'(les) auteur(s) |
|---|