Spectral Estimation Problem in Infinite Dimensional Spaces

TL;DR

This paper addresses the spectral estimation problem in infinite dimensional spaces, employing boundary control methods to solve inverse problems and applying these techniques to hyperbolic systems.

Contribution

Introduces a boundary control approach to spectral estimation in infinite dimensions, extending inverse theory methods to new classes of problems.

Findings

Successfully solves the spectral estimation problem in infinite-dimensional spaces.

Demonstrates application to initial boundary value problems for hyperbolic systems.

Provides a new framework for inverse spectral problems in complex systems.

Abstract

We consider the generalized spectral estimation problem in infinite dimensional spaces. We solve this problem using the boundary control approach to inverse theory and provide an application to the initial boundary value problem for a hyperbolic system.