INVERSE PROBLEM FOR A CLASS OF DIRAC OPERATOR

In this paper, we consider a problem for the first order canonical Dirac differential equations system with piecewise continuous coefficient and spectral parameter dependent in boundary condition. The asymptotic behavior of eigenvalues, eigenfunctions and normalizing numbers of this system is investigated. The completeness theorem is proved. The spectral expansion formula with respect to eigenvector functions or equivalently Parseval equality is obtained. Weyl solution and Weyl function for the problem are constructed. Uniqueness theorem for inverse problem by the Weyl function and by the spectral data are proved. 2010Mathematics Subject Classification: 34A55, 34L40, 34L10. Key words and phrases: Dirac operator, Weyl function, Inverse problem, Expansion formula.