Inverse nodal problems for Dirac-type integro-differential operators

TL;DR

This paper investigates the inverse nodal problem for Dirac-type integro-differential operators, demonstrating that nodal points uniquely determine the operator's coefficients and providing a reconstruction algorithm.

Contribution

It introduces a method to uniquely recover coefficients of Dirac-type integro-differential operators from nodal data, including a reconstruction algorithm.

Findings

Dense subset of nodal points determines the coefficients.

Proved a uniqueness theorem for the inverse problem.

Developed an algorithm for coefficient reconstruction.

Abstract

The inverse nodal problem for Dirac differential operator perturbated by a Volterra integral operator is studied. We prove that dense subset of the nodal points determines the coefficients of differential and integral part of the operator. We also provide a uniqueness theorem and an algorithm to reconstruct the coefficients of the problem by using the nodal points.