Inverse problems for discontinuous Dirac operator with eigenparameter dependent boundary and transmission conditions

Abstract

In this study, we consider the discontinuous Dirac equations system with eigenparameter dependent boundary and finite number of transmission conditions. First, the space that corresponds to problem is introduced, the norm on this space is defined and the operator model that corresponds to the given problem is constructed on this space. Then the integral equations and asymptotics of eigenfunctions of the problem are obtained. The characteristic function is defined and the asymptotic formula of the characteristic function is given by using obtained asymptotics of eigenfunctions. After the Weyl solution and the Weyl function of the problem are formed. Finally, some uniqueness theorems are proved by using Weyl function and some spectral data.