Gluing semiclassical resolvent estimates via propagation of singularities

Abstract

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 Schrödinger 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 Schrödinger propagator.

26 pages, 1 figure

References in corpus (2)

• Resolvent estimates for normally hyperbolic trapped sets
• Local smoothing for scattering manifolds with hyperbolic trapped sets

Cited by in corpus (9)

• Semilinear wave equations on asymptotically de Sitter, Kerr-de Sitter and Minkowski spacetimes
• Local Energy Decay for the Damped Wave Equation
• Spectral gaps for normally hyperbolic trapping
• Stochastic stability of Pollicott-Ruelle resonances
• Global analysis of quasilinear wave equations on asymptotically Kerr-de Sitter spaces
• The Feynman propagator on perturbations of Minkowski space
• Spectral gap for obstacle scattering in dimension 2
• Resonance free regions for nontrapping manifolds with cusps
• Semiclassical propagation through cone points