Resolvent estimates for non-self-adjoint operators via semi-groups
Spectral Theory
2009-06-02 v1 Analysis of PDEs
Abstract
We consider a non-self-adjoint -pseudodifferential operator in the semi-classical limit (). If is the leading symbol, then under suitable assumptions about the behaviour of at infinity, we know that the resolvent is uniformly bounded for in any compact set not intersecting the closure of the range of . Under a subellipticity condition, we show that the resolvent extends locally inside the range up to a distance from certain boundary points, where . This is a slight improvement of a result by Dencker, Zworski and the author, and it has recently been obtained by W. Bordeaux Montrieux in a model situation where . The method of proof is different from the one of Dencker et al, and is based on estimates of an associated semi-group.
Cite
@article{arxiv.0906.0094,
title = {Resolvent estimates for non-self-adjoint operators via semi-groups},
author = {Johannes Sjoestrand},
journal= {arXiv preprint arXiv:0906.0094},
year = {2009}
}