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

Abstract

In this study, we consider the discontinuous Dirac equationssystem with eigenparameter dependent boundary and finitenumber of transmission conditions. First, the space thatcorresponds to problem is introduced, the norm on thisspace is defined and the operator model that correspondsto the given problem is constructed on this space. Thenthe integral equations and asymptotics of eigenfunctionsof the problem are obtained. The characteristic functionis defined and the asymptotic formula of the character-istic function is given by using obtained asymptotics ofeigenfunctions. After the Weyl solution and the Weylfunction of the problem are formed. Finally, some unique-ness theorems are proved by using Weyl function and somespectral data.