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

Yaniv Almog (1) , B Helffer (2)

1 LSU - Louisiana State University
2 LMJL - Laboratoire de Mathématiques Jean Leray

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.

Domaines: Mathématiques [math]

Yaniv Almog, B Helffer. On the spectrum of non-selfadjoint Schrödinger operators with compact resolvent. Communications in Partial Differential Equations, 2015, 40 (8), pp.1441-1466. ⟨hal-01431683⟩