Gluing semiclassical resolvent estimates, or the importance of being microlocal

Details Gluing semiclassical resolvent estimates, or the importance of being microlocal Gluing semiclassical resolvent estimates, or the importance of being microlocal

2010-08-24

arxiv.org/abs/1008.3964v1

Mathematics

Analysis of PDEs

20 pages, 1 figure

Scientific paper

We use semiclassical propagation of singularities to give a general method for gluing together resolvent estimates. As an application we prove estimates for the analytic continuation of the resolvent of a Schr\"odinger operator for certain asymptotically hyperbolic manifolds in the presence of trapping which is sufficiently mild in one of several senses. As a corollary we obtain local exponential decay for the wave propagator and local smoothing for the Schr\"odinger propagator.

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