On recovering Sturm-Liouville differential operators with deviating argument

TL;DR

This paper investigates the spectral properties of second-order functional differential operators with constant delay and introduces a unique, constructive method for solving the inverse problem of recovering these operators from their spectra.

Contribution

It provides a new uniqueness theorem and a constructive algorithm for recovering Sturm-Liouville operators with deviating argument from spectral data.

Findings

Established spectral properties of delayed differential operators.

Proved uniqueness of the inverse spectral problem.

Developed a constructive solution algorithm.

Abstract

We consider second-order functional differential operators with a constant delay. Properties of their spectral characteristics are obtained and a nonlinear inverse problem is studied, which consists in recovering the operators from their spectra. We establish the uniqueness and develop a constructive algorithm for solution of the inverse problem.