Reconstruction of the Dirac-Type Integro-Differential Operator from Nodal Data

TL;DR

This paper investigates how to reconstruct the coefficients of a Dirac-type integro-differential operator using nodal data, demonstrating that a dense subset of nodal points can determine the differential coefficients and partially reveal the integral part.

Contribution

It introduces a method to recover the differential coefficients from nodal data for Dirac-type integro-differential operators, including partial information about the integral component.

Findings

Dense subset of nodal points determines differential coefficients.

Partial information about the integral part can be obtained.

Reconstruction method applicable to Dirac-type integro-differential operators.

Abstract

The inverse nodal problem for Dirac type integro-differential operator with the spectral parameter in the boundary conditions is studied. We prove that dense subset of the nodal points determines the coefficients of differential part of operator and gives partial information for integral part of it.