On the construction of de Branges spaces for dynamical systems associated with finite Jacobi matrices

TL;DR

This paper explores how to construct de Branges spaces for dynamical systems linked to finite Jacobi matrices, providing a mathematical framework for analyzing such systems.

Contribution

It introduces a novel method to associate de Branges spaces with boundary-controlled dynamical systems based on finite Jacobi matrices.

Findings

Established a new construction method for de Branges spaces

Connected spectral properties of Jacobi matrices with analytic function spaces

Provided insights into boundary control systems analysis

Abstract

We consider dynamical systems with boundary control associated with finite Jacobi matrices. Using the method previously developed by the authors, we associate with these systems special Hilbert spaces of analytic functions (de Branges spaces)