The Asymptotic Trace Of Dirac Eigenvalue Problem With Unlocal Boundary Conditions

Let The equation is called one-dimensional Dirac equation. In this paper, the asymptotic traces of Dirac eigenvalue problem with unlocal boundary conditions are researched .The boundary conditions are following:First, an entire functionω(λ) is constructed by use of the asymptotic estimations of solution of initial value problem for Dirac equation.The zeros ofω(λ) are the eigenvalues of Dirac eigenvalue problem with unlocal boundary conditions.Then, by resorting to the identity using the residue method,we estimate the Dirac operator eigenvalue and obtain the eigenvalue's asymptotic trace identities of two boundary problems.