Pollicott-Ruelle resolvent and Sobolev regularity
Dynamical Systems
2023-04-25 v2 Analysis of PDEs
Abstract
In this note we compute the threshold regularity for meromorphic continuation of the Pollicott--Ruelle resolvent of an Anosov flow as an operator on anisotropic Sobolev spaces, in the setting of lifts to general vector bundles. These thresholds are related to the Sobolev regularity needed for the decay of correlations.
Cite
@article{arxiv.2108.06611,
title = {Pollicott-Ruelle resolvent and Sobolev regularity},
author = {Semyon Dyatlov},
journal= {arXiv preprint arXiv:2108.06611},
year = {2023}
}
Comments
30 pages; minor revisions following the referee's suggestions. To appear in the special issue of PAFA in honor of Louis Nirenberg