On an application of the Boundary control method to classical moment problems

TL;DR

This paper connects classical moment problems with boundary control methods, showing that solving truncated moment problems is equivalent to addressing generalized spectral problems in dynamical systems.

Contribution

It introduces a novel approach linking moment problems to boundary control methods for discrete-time systems with Jacobi matrices.

Findings

Established relationships between moment problems and boundary control.

Demonstrated equivalence of truncated moment problems to spectral problems.

Provided a new framework for solving classical moment problems.

Abstract

We establish relationships between the classical moments problems which are problems of a construction of a measure supported on a real line, on a half-line or on an interval from prescribed set of moments with the Boundary control approach to a dynamic inverse problem for a dynamical system with discrete time associated with Jacobi matrices. We show that the solution of corresponding truncated moment problems is equivalent to solving some generalized spectral problems.