English

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.

Keywords

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

R2 v1 2026-06-21T16:26:53.280Z