On recovering Dirac operators with two delays

TL;DR

This paper investigates the inverse spectral problem for Dirac-type operators with two delays, establishing conditions under which the operator can be uniquely recovered from spectral data.

Contribution

It proves unique recovery of Dirac operators with two delays from four spectra under specific delay conditions, extending inverse spectral theory.

Findings

Unique recovery from four spectra when $2a_1+\frac{a_2}{2}\geq \pi$

Non-uniqueness when the condition is not met

Conditions relate delays to spectral data for operator reconstruction

Abstract

We study the inverse spectral problems of recovering Dirac-type functional-differential operator with two constant delays $a_1$ and $a_2$ not less than one-third of the interval. It has been proved that the operator can be recovered uniquely from four spectra under the condition $2a_1+\frac{a_2}{2}\geq \pi$, while it is not possible otherwise.