# On the relationship between Weyl functions of Jacobi matrices and response vectors for special dynamical systems with discrete time

## TL;DR

This paper establishes a novel connection between Weyl functions of Jacobi matrices and response vectors of specific discrete-time dynamical systems, providing new insights into their spectral properties.

## Contribution

It introduces a special representation for Weyl functions of finite and semi-infinite Jacobi matrices based on their relationship with dynamical systems.

## Key findings

- Derived a new representation for Weyl functions.
- Linked spectral problems with initial-boundary value problems.
- Applicable to bounded Jacobi matrices.

## Abstract

We derive special representation for Weyl functions for finite and semi-infinite Jacobi matrices with bounded entries based on a relationship between spectral problem for Jacobi matrices and initial-boundary value problem for auxiliary dynamical systems with the discrete time for Jacobi matrices.