Recovering Dirac systems with singularities in interior points

TL;DR

This paper investigates inverse spectral problems for Dirac systems with interior singularities, establishing spectral properties, uniqueness, and a constructive solution method for the inverse problem.

Contribution

It introduces a novel approach to reconstruct Dirac systems with interior singularities, proving uniqueness and providing conditions for solvability.

Findings

Spectral properties of Dirac systems with singularities are characterized.

A constructive method for solving the inverse spectral problem is developed.

Uniqueness of the inverse problem solution is established.

Abstract

We study the non-selfadjoint Dirac system on a finite interval having non-integrable regular singularities in interior points with additional matching conditions at these points. Properties of spectral characteristics are established, and the inverse spectral problem is investigated. We provide a constructive procedure for the solution of the inverse problem, and prove its uniqueness. Moreover, necessary and sufficient conditions for the global solvability of this nonlinear inverse problem are obtained.