非连续Dirac算子谱的分布及其逆谱问题

The Distribution of the Spectra and the Inverse Problem for the Discontinuous Dirac Operator

本文考虑了定义在[0,1]区间上,在点to∈(0,1)具有界面条件的Dirac算子的特征值与定义在子区间[0,t_0],[t_0,1]上的两个Dirac算子的特征值及其逆特征值问题.利用WeylTitchmarsh-m-函数的单调性态,给出了这三组谱之间的交错性关系,证明了若子区间上的两组谱不交,则势函数对(p(x),r(x))和边值条件中的参数h,H可由这三组谱唯一确定.

In this paper, we consider the eigenvalue and the inverse eigenvalue problem of the Dirac operator defined on [0, 1], which has the jump conditions on to∈ （0, 1） and two Dirac operators defined respectively on subset [0, to] and [to, 1], by using the monotonicity of the Weyl-Titchmarsh-m-function, the alternation of the three spectra is considered, we prove that the pair of potentials （p（x）, r（x）） and the parameter h, H in the boundary conditions can be uniquely determined by the three spectra if the two spectra of the operators defined on subsets are disioint.