Spectral averaging techniques for Jacobi matrices

TL;DR

This paper revisits and extends spectral averaging methods for Jacobi matrices, focusing on multiple parameter averaging and establishing lower bounds on spectral measure densities to analyze stability under perturbations.

Contribution

It introduces extended spectral averaging techniques for Jacobi matrices, including simultaneous parameter averaging and new Wegner type estimates for spectral measure densities.

Findings

Established lower bounds on spectral measure densities.

Analyzed stability of spectral types under local perturbations.

Extended spectral averaging methods to multiple parameters.

Abstract

Spectral averaging techniques for one-dimensional discrete Schroedinger operators are revisited and extended. In particular, simultaneous averaging over several parameters is discussed. Special focus is put on proving lower bounds on the density of the averaged spectral measures. These Wegner type estimates are used to analyze stability properties for the spectral types of Jacobi matrices under local perturbations.