Inverse problems for finite Jacobi matrices and Krein--Stieltjes strings

TL;DR

This paper develops three methods to solve inverse problems for finite Jacobi matrices and Krein-Stieltjes strings using dynamic Dirichlet-to-Neumann data, and characterizes the inverse data for these systems.

Contribution

It introduces new techniques for recovering system parameters from dynamic boundary measurements in finite Jacobi and Krein-Stieltjes systems.

Findings

Three methods for parameter recovery from inverse data.

Characterization of dynamic inverse data for both systems.

Enhanced understanding of inverse problems in finite spectral systems.

Abstract

We consider dynamic inverse problems for a dynamical system associated with a finite Jacobi matrix and for a system describing propagation of waves in a finite Krein-Stieltjes string. We offer three methods of recovering unknown parameters: entries of a Jacobi matrix in the first problem and point masses and distances between them in the second, from dynamic Dirichlet-to-Neumann operators. We also answer a question on a characterization of dynamic inverse data for these two problems.