Bohr-Sommerfeld quantization conditions for non-selfadjoint perturbations of selfadjoint operators in dimension one
Spectral Theory
2015-11-20 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
In this paper, we give a description of the spectrum of a class of non-selfadjoint perturbations of selfadjoint operators in dimension one and we show that it is given by Bohr-Sommerfeld quantization conditions. To achieve this, we make use of previous work by Michael Hitrik, Anders Melin and Johannes Sj{\"o}strand. We also give an application of our result in the case of PT-symmetric pseudo-differential operators.
Keywords
Cite
@article{arxiv.1511.06237,
title = {Bohr-Sommerfeld quantization conditions for non-selfadjoint perturbations of selfadjoint operators in dimension one},
author = {Ophélie Rouby},
journal= {arXiv preprint arXiv:1511.06237},
year = {2015}
}