Propagation through trapped sets and semiclassical resolvent estimates
Analysis of PDEs
2013-08-28 v2
Abstract
Motivated by the study of resolvent estimates in the presence of trapping, we prove a semiclassical propagation theorem in a neighborhood of a compact invariant subset of the bicharacteristic flow which is isolated in a suitable sense. Examples include a global trapped set and a single isolated periodic trajectory. This is applied to obtain microlocal resolvent estimates with no loss compared to the nontrapping setting.
Cite
@article{arxiv.1010.2190,
title = {Propagation through trapped sets and semiclassical resolvent estimates},
author = {Kiril Datchev and András Vasy},
journal= {arXiv preprint arXiv:1010.2190},
year = {2013}
}
Comments
25 pages, 6 figures