Spectral analysis of a class of hermitian Jacobi matrices in a critical (double root) hyperbolic case

TL;DR

This paper analyzes the spectral properties of a specific class of hermitian Jacobi matrices with periodic modulation in a critical hyperbolic case, providing asymptotics of eigenvectors and spectrum analysis.

Contribution

It introduces a new approach to analyze hermitian Jacobi matrices in a critical hyperbolic case, extending existing theorems for broader applicability.

Findings

Asymptotics of generalized eigenvectors derived

Spectrum characterized in the critical hyperbolic case

Reformulation of a key theorem for spectral analysis

Abstract

We consider a class of Jacobi matrices with periodically modulated diagonal in a critical hyperbolic ("double root") situation. For the model with "non-smooth" matrix entries we obtain the asymptotics of generalized eigenvectors and analyze the spectrum. In addition, we reformulate a very helpful theorem from a paper of Janas and Moszynski in its full generality in order to serve the needs of our method.