An inverse problem for the integro-differential Dirac system with partial information given on the convolution kernel

TL;DR

This paper addresses an inverse problem for a Dirac system with convolution, aiming to recover the unknown kernel on a full interval using partial spectral data and known kernel segments.

Contribution

It introduces a uniqueness theorem, an algorithm for kernel recovery, and conditions for solvability when the convolution kernel is partially known.

Findings

Proved uniqueness of kernel recovery under given conditions

Developed an algorithm for reconstructing the kernel

Established necessary and sufficient conditions for solution existence

Abstract

An integro-differential Dirac system with an integral term in the form of convolution is considered. We suppose that the convolution kernel is known a priori on a part of the interval, and recover it on the remaining part, using a part of the spectrum. We prove the uniqueness theorem, provide an algorithm for the solution of the inverse problem together with necessary and sufficient conditions for its solvability.