Dirac Operator Eigenvalue Problem And Its Boundary Value Problem Of Kramer Analytic Nuclear

In this paper, we discuss the classification of self-adjoint boundary conditionsfor regular Dirac operators. We also study the multiplicity of the eigenvalues of Diracoperators and the application of the Kramer Sampling theorem to Dirac problems withcoupled boundary condition. The main results as following:First, we give the canonical representations of self-adjoint boundary conditions forDirac operators, ie. separated self-adjoint boundary condition and coupled self-adjointboundary condition.Second, just as the case of separated self-adjoint boundary condition, we prove theequality between the geometric multiplicity and algebraie multiplicity of eigenvalues ofthe Dirac operator with coupled self-adjoint boundary condition.Third, under the condition of the equality between the geometric multiplicityand algebraic multiplicity of eigenvalues of regular Dirac operators, we show that theKramer analytic kernels exist, for which, there exists at least one eigenvalue of multi-plicity 2 for Dirac operators with coupled boundary condition.