Resolvent Estimates for the Laplacian on Asymptotically Hyperbolic Manifolds

Combining results of Cardoso-Vodev [6] and Froese-Hislop [9], we use Mourre’s theory to prove high energy estimates for the boundary values of the weighted resolvent of the Laplacian on an asymptotically hyperbolic manifold. We derive estimates involving a class of pseudo-differential weights which are more natural in the asymptotically hyperbolic geometry than the weights used in [6]. submitted 28/04/05, accepted 26/09/05