Inverse Problems For Dirac Operators With a Finite Number of Transmission Conditions

TL;DR

This paper studies a discontinuous Dirac operator with polynomial spectral dependence and transmission conditions, analyzing eigenvalues, eigenfunctions, and establishing uniqueness theorems using spectral data and Weyl functions.

Contribution

It introduces new spectral analysis results for Dirac operators with transmission conditions and polynomial spectral dependence, including eigenvalue properties and uniqueness theorems.

Findings

Properties of eigenvalues and eigenfunctions are established.

Uniqueness theorems are proved using Weyl functions and spectral data.

Abstract

In this paper, we consider a discontinuous Dirac operator depending polynomially on the spectral parameter and a finite number of transmission conditions. We get some properties of eigenvalues and eigenfunctions. Then, we investigate some uniqueness theorems by using Weyl function and some spectral data.