On complex perturbations of infinite band Schrodinger operators

TL;DR

This paper investigates how complex perturbations affect the spectrum of infinite band Schrödinger operators, providing inequalities that describe the convergence rate of the discrete spectrum to the essential spectrum.

Contribution

It introduces Lieb–Thirring type inequalities for the spectral convergence of perturbed infinite band Schrödinger operators, extending spectral analysis in complex perturbation contexts.

Findings

Derived inequalities for spectral convergence rates

Quantified the impact of complex perturbations on the spectrum

Extended spectral theory for infinite band Schrödinger operators

Abstract

We study a complex perturbation of a self-adjoint infinite band Schrodinger operator (defined in the form sense), and obtain the Lieb--Thirring type inequalities for the rate of convergence of the discrete spectrum of the perturbed operator to the joint essential spectrum of both operators.