Analytic continuation and semiclassical resolvent estimates on asymptotically hyperbolic spaces

Abstract

In this paper we construct a parametrix for the high-energy asymptotics of the analytic continuation of the resolvent on a Riemannian manifold which is a small perturbation of the Poincaré metric on hyperbolic space. As a result, we obtain non-trapping high energy estimates for this analytic continuation.

46 pages, 4 figures

References in corpus (2)

• The wave equation on Schwarzschild-de Sitter spacetimes
• Asymptotics of solutions of the wave equation on de Sitter-Schwarzschild space