# Dynamical inverse problem for Jacobi matrices

## TL;DR

This paper addresses the inverse dynamical problem for semi-infinite Jacobi matrices, providing a solution and characterization of inverse data, along with conditions for spectral measures of discrete Schrödinger operators.

## Contribution

It offers a novel solution to the inverse problem for Jacobi matrices and characterizes inverse data and spectral measures.

## Key findings

- Solved the inverse problem for the dynamical system with Jacobi matrices.
- Provided necessary and sufficient conditions for spectral measures.
- Characterized inverse data for semi-infinite Jacobi matrices.

## Abstract

We consider the inverse dynamical problem for the dynamical system with discrete time associated with the semi-infinite Jacobi matrix. We solve the inverse problem for such a system and answer a question on the characterization of the inverse data. As a by-product we give a necessary and sufficient condition for the measure on the real line line to be the spectral measure of semi-infinite discrete Schrodinger operator.