Lieb-Thirring Inequalities for Complex Finite Gap Jacobi Matrices

TL;DR

This paper derives Lieb-Thirring inequalities for the eigenvalues of complex perturbations of finite gap Jacobi matrices, extending spectral bounds to a broader class of operators.

Contribution

It introduces Lieb-Thirring bounds for complex finite gap Jacobi matrices, generalizing previous results to Schatten class perturbations.

Findings

Established power bounds on discrete eigenvalues

Extended Lieb-Thirring inequalities to complex perturbations

Applicable to finite gap Jacobi matrices

Abstract

We establish Lieb-Thirring power bounds on discrete eigenvalues of Jacobi operators for Schatten class complex perturbations of periodic and more generally finite gap Jacobi matrices.