Spectral Density of Jacobi Matrices with small deviations

TL;DR

This paper develops new asymptotic trace formulas for Jacobi matrices with small deviations, extending existing formulas and providing deeper insights into their spectral density behavior.

Contribution

Introduces novel asymptotic trace formulas for Jacobi matrices under small deviation conditions, broadening the scope of spectral analysis techniques.

Findings

Extended existing trace formulas to more general Jacobi matrices.

Derived asymptotic expressions for spectral density.

Enhanced understanding of spectral properties with small coefficient deviations.

Abstract

We present several new asymptotic trace formulas for Jacobi matrices whose coefficients satisfy a small deviation condition. Our results extend most of the existing trace formulas for Jacobi matrices.