Asymptotics of large eigenvalues for a class of band matrices

TL;DR

This paper studies the asymptotic behavior of large eigenvalues in a specific class of finite difference self-adjoint operators with compact resolvent, providing insights into their spectral properties.

Contribution

It offers new asymptotic formulas for large eigenvalues of a class of band matrices, advancing understanding of their spectral characteristics.

Findings

Derived asymptotic formulas for large eigenvalues.

Identified spectral properties of the class of band matrices.

Enhanced understanding of eigenvalue distribution in finite difference operators.

Abstract

We investigate the asymptotic behaviour of large eigenvalues for a class of finite difference self-adjoint operators with compact resolvent in $l^2$.