Semiclassical estimates in asymptotically Euclidean scattering

Details Semiclassical estimates in asymptotically Euclidean scattering Semiclassical estimates in asymptotically Euclidean scattering

1999-10-19

arxiv.org/abs/math/9910098v1

Mathematics

Analysis of PDEs

11 pages, 4 figures, AMS Latex

Scientific paper

10.1007/s002200000207

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.

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