On the spectrum of non-selfadjoint Schrödinger operators with compact resolvent

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 Schrödinger 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.

References in corpus (2)

• On the reality of the eigenvalues for a class of PT-symmetric oscillators
• On the metric operator for the imaginary cubic oscillator

Cited by in corpus (1)

• Compactness Criteria for the Resolvent of the Fokker-Planck operator