Gluing Semiclassical Resolvent Estimates via Propagation of Singularities

By K. Datchev, András Vasy. 2010

62 citations recorded by the source corpus.

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.

Subfields: Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d7fc54470ec231efb077eda918e229043c6a06fb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. P. Hintz
2. András Vasy

Citations in the corpus

• Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces (with an appendix by Semyon Dyatlov) (2010, methodology): “3, the resolvent is semiclassically outgoing with a loss of h, in the sense of recent results of Datchev and Vasy [15] and [16].”
• The global non-linear stability of the Kerr-de Sitter family of black holes (2016, background): “A precise study in the spirit of [140] and [46] is currently in progress [67].”