Trace Identities of Non-Self-Adjoint Dirac Operators

Abstract:

      This paper deals with asymptotic trace of non-self-adjoint Dirac operator eigenvalue problem with two points linear boundary condition. The asymptotic eatimations of solution of Cauchy problem are obtained for Dirac equation by use of the transformation matrix operator. By constructing an entire function $\omega(\lambda)$, and discussing every term's coefficient of $\omega(\lambda)$, boundary conditions are turned into eight element types. By resorting the residue method, four types eigenvalue's trace identities are obtained.