一类边界条件中含谱参数的Dirac算子的谱性质

Spectral Properties of a Class of Dirac Operators with Eigenparameter in the Boundary Conditions

摘要: 本文考虑了一类内部具有两个不连续点且边界条件依赖谱参数的Dirac算子的谱性质。首先通过引入适当的Hilbert空间并在其上定义新的自伴算子，使得所考虑问题的特征值与该算子的特征值一致。然后通过构造基本解得到了特征值的一些性质。最后给出了问题的Green函数和预解算子。

Abstract: In this paper, we consider the spectral properties of a class of Dirac operators with two internal discontinuities and spectral parameter-dependent boundary conditions. First, the eigenvalues of the problem under consideration are made to coincide with the eigenvalues of the operator by introducing a suitable Hilbert space and defining a new self-adjoint operator on it. Then some properties of the eigenvalues are obtained by constructing the basic solution. Finally, Green’s function and the resolvent operator of the problem are given.