On Discontinuous Dirac Operator with Eigenparameter Dependent Boundary and Two Transmission Conditions

TL;DR

This paper studies a discontinuous Dirac operator with eigenparameter-dependent boundary and transmission conditions, analyzing spectral properties, Green's function, and resolvent operator to establish foundational results.

Contribution

It introduces a Hilbert space framework for such operators and explores spectral properties, Green's function, and uniqueness theorems, advancing understanding of these complex boundary-value problems.

Findings

Eigenvalues and eigenfunctions have specific properties under the given conditions.

Green's function and resolvent operator are explicitly characterized.

Uniqueness theorems are established using Weyl function and spectral data.

Abstract

In this paper, we consider a discontinuous Dirac operator with eigenparameter dependent both boundary and two transmission conditions. We introduce a suitable Hilbert space formulation and get some properties of eigenvalues and eigenfunctions. Then, we investigate Green's function, resolvent operator and some uniqueness theorems by using Weyl function and some spectral data.