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

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.

References in corpus (5)

• The boundary control approach to the Titchmarsh-Weyl $m-$function
• The boundary control approach to inverse spectral theory
• Unified approach to classical equations of inverse problem theory
• Dynamical inverse problem for the discrete Schrödinger operator
• Relationship between different types of inverse data for the one-dimensional Schrödinger operator on a half-line

Cited by in corpus (4)

• On an application of the Boundary control method to classical moment problems
• Construction of solutions of Toda lattices by the classical moment problem
• Inverse problems for finite Jacobi matrices and Krein--Stieltjes strings
• Discrete dynamical systems: inverse problems and related topics