Lieb-Thirring Inequalities for Finite and Infinite Gap Jacobi Matrices

TL;DR

This paper derives Lieb-Thirring inequalities for eigenvalues of Jacobi matrices, including finite and infinite gap cases, under broad Schatten class perturbations, extending previous spectral bounds to more general operators.

Contribution

It introduces Lieb-Thirring bounds for Jacobi operators with complex spectra, including reflectionless and Cantor-type spectra, under general Schatten class perturbations.

Findings

Lieb-Thirring bounds established for finite and infinite gap Jacobi matrices.

Results apply to reflectionless operators with complex spectra.

Provides spectral bounds under broad perturbation conditions.

Abstract

We establish Lieb-Thirring power bounds on discrete eigenvalues of Jacobi operators for Schatten class perturbations under very general assumptions. Our results apply, in particular, to perturbations of reflectionless Jacobi operators with finite gap and Cantor-type essential spectrum.