English

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}
}