Abstract.
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 \( \langle r\rangle ^{{ - 1/2 - \in }} \) used in [6].
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Communicated by Bernard Helffer
submitted 28/04/05, accepted 26/09/05
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Bouclet, JM. Resolvent Estimates for the Laplacian on Asymptotically Hyperbolic Manifolds. Ann. Henri Poincaré 7, 527–561 (2006). https://doi.org/10.1007/s00023-005-0259-z
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DOI: https://doi.org/10.1007/s00023-005-0259-z