Spectral enclosures and stability for non-self-adjoint discrete Schroedinger operators on the half-line

TL;DR

This paper analyzes the spectral properties and stability of non-self-adjoint discrete Schrödinger operators on the half-line, providing optimal enclosures, stability conditions, and Hardy inequalities for complex potentials and boundary conditions.

Contribution

It introduces new spectral enclosures, stability criteria, and Hardy inequalities for non-self-adjoint discrete Schrödinger operators with complex potentials and boundary conditions.

Findings

Optimal spectral enclosures for summable potentials.

Conditions for spectral stability under small potentials.

Discrete Hardy inequalities for the Dirichlet Laplacian.

Abstract

We make a spectral analysis of discrete Schroedinger operators on the half-line, subject to complex Robin-type boundary couplings and complex-valued potentials. First, optimal spectral enclosures are obtained for summable potentials. Second, general smallness conditions on the potentials guaranteeing a spectral stability are established. Third, a general identity which allows to generate optimal discrete Hardy inequalities for the discrete Dirichlet Laplacian on the half-line is proved.