The Eigenvalue Problems Of Regular Dirac Operator

By resorting to the residue method, the asymptotic formulas for the eigenvalues and the expansion theorems of Dirac eigenvalue problems are proved under the self-adjoint and non- self-adjoint boundary conditions. For the expansion theorems of self- adjoint Dirac operator, it is difficult to prove it by using the method of integral equation. In this paper, we clearly and strictly prove the asymptotic formulas for the eigenvalues and the expansion theorems. The condition under which the Dirac operator is self-adjoint is discussed under the general linear boundary condition between the interval of two points. For the expansion theorem of non-self-adjoint Dirac operator, it is unable to use the method of integral equation. But under the linear boundary condition and unlocal boundary condition, the eigenvalue expansion problems of non-self-adjoint operator can still be discussed by using the residue method. For the non-self-adjoint Dirac operators, there are plentiful content in the problems of eigenvalue expansion problems. Besides, the eigenvalue trace formula of Dirac operator under unlocal boundary condition is obtained .