Semiclassical estimates in asymptotically Euclidean scattering
arXiv:math/9910098 · doi:10.1007/s002200000207
Abstract
In this note we obtain semiclassical resolvent estimates for non-trapping long range perturbations of the Laplacian on asymptotically Euclidean manifolds. Our proof is based on a positive commutator argument which differs from Mourre-type estimates by making the commutant also positive. The resolvent estimates, including the weighting of the Sobolev spaces in the estimates, are an immediate consequence.
11 pages, 4 figures, AMS Latex