Leonid Golinskii (University of Kharkiv)

On distribution of the discrete spectrum for non-self-adjoint Schrödinger operators on the half-line and Jacobi operators.

Abstract:

We study the quantitative structure of the discrete spectrum for non-self-adjoint (NSA) Schrödinger operators on the half-line with the Dirichlet boundary condition and NSA semi-infinite Jacobi operators. We prove upper and lower bounds for sums of eigenvalues of the Lieb–Thirring type for such operators. The upper bounds are established for general classes of complex, integrable potentials and are shown to be optimal in various senses by proving the lower bounds for specific potentials. Based on the joint paper with A. Stepanenko arXiv:2111.09629.