Periodic perturbations of unbounded Jacobi matrices I: Asymptotics of generalized eigenvectors

TL;DR

This paper investigates the asymptotic behavior of generalized eigenvectors for Jacobi matrices, establishing conditions for self-adjointness and non-subordinacy under weak coefficient assumptions.

Contribution

It provides new criteria for self-adjointness and non-subordinacy of Jacobi matrices with unbounded coefficients, enhancing understanding of their spectral properties.

Findings

Identifies conditions for self-adjointness of Jacobi matrices

Establishes strong non-subordinacy under weak coefficient assumptions

Analyzes asymptotics of generalized eigenvectors

Abstract

We study asymptotics of generalized eigenvectors associated with Jacobi matrices. Under weak conditions on the coefficients we identify when the matrices are self-adjoint and show that they satisfy strong non-subordinacy condition.