Boundary Control method and De Branges spaces. Schrödinger equation, Dirac system and Discrete Schrödinger operator

Abstract

In the framework of the application of the Boundary Control method to solving the inverse dynamical problems for the one-dimensional Schrödinger and Dirac operators on the half-line and semi-infinite discrete Schrödinger operator, we establish the connections with the method of De Branges: for each of the system we construct the De Branges space and give a natural dynamical interpretation of all its ingredients: the set of function the De Brange space consists of, the scalar product, the reproducing kernel.

References in corpus (7)

• Canonical systems and de Branges spaces
• 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
• Inverse problem for one-dimensional dynamical Dirac system (BC-method)
• 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 (6)

• On the relationship between Weyl functions of Jacobi matrices and response vectors for special dynamical systems with discrete time
• On an application of the Boundary control method to classical moment problems
• Forward and inverse problems for a finite Krein-Stieltjes string. Approximation of constant density by point masses
• 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