On some applications of the Boundary Control method to spectral estimation and inverse problems

TL;DR

This paper explores how the Boundary Control method can be applied to spectral estimation and inverse source problems, emphasizing the importance of controllability and exponential family properties for solvability.

Contribution

It derives the BC method equations for these problems and analyzes the conditions affecting their solvability, advancing the theoretical framework for inverse spectral problems.

Findings

Solvability depends on controllability of the dynamical system.

Properties of exponential families influence the BC method's effectiveness.

Provides new equations for applying BC to spectral and inverse problems.

Abstract

We consider applications of the Boundary Control (BC) method to generalized spectral estimation problems and to inverse source problems. We derive the equations of the BC method for this problems and show that solvability of this equations crucially depends on the controllability properties of the corresponding dynamical system and properties of corresponding families of exponentials.