On the spectrum of non-selfadjoint Schr\"odinger operators with compact resolvent
Mathematical Physics
2014-10-21 v1 math.MP
Abstract
We determine the Schatten class for the compact resolvent of Dirichlet realizations, in unbounded domains, of a class of non-selfadjoint differential operators. This class consists of operators that can be obtained via analytic dilation from a Schr\"odinger operator with magnetic field and a complex electric potential. As an application, we prove, in a variety of examples motivated by Physics, that the system of generalized eigenfunctions associated with the operator is complete, or at least the existence of an infinite discrete spectrum.
Keywords
Cite
@article{arxiv.1410.5122,
title = {On the spectrum of non-selfadjoint Schr\"odinger operators with compact resolvent},
author = {Yaniv Almog and Bernard Helffer},
journal= {arXiv preprint arXiv:1410.5122},
year = {2014}
}