Inverse Problem for a Class of Dirac Operators with Spectral Parameter Contained in Boundary Conditions

Abstract

This paper is related to an inverse problem for a class of Dirac operators with discontinuous coefficient and eigenvalue parameter contained in boundary conditions. The asymptotic formula of eigenvalues of this problem is examined. The theorem on completeness of eigenfunctions is proved. The expansion formula with respect to eigenfunctions is obtained and Parseval equality is given. Weyl solution and Weyl function are constructed. Uniqueness theorem of the inverse problem respect to the Weyl function is proved.