有限区间上Dirac算子的谱逆问题
Inverse spectral problems for Dirac operators on a finite interval
摘要：
本文考虑由微分表达式$$ \mathfrak t_q:=\frac{1}{i}[I&0 0&-I]\frac{d}{dx}+[0&q q^*&0] $$和一些分离的边界条件生成的Dirac算子的正谱问题和逆谱问题。这里，$q$是一个$r\times r$矩阵值函数，其条目属于$L_2((0,1),\mathbb C)$，$I$是单位$r\times r$矩阵。我们给出了一个完整的描述的光谱数据（特征值和适当引入的赋范矩阵）的运营商正在考虑和建议的算法重建潜在的$q$从相应的光谱数据。
英文摘要：
We consider the direct and inverse spectral problems for Dirac operators that are generated by the differential expressions $$ \mathfrak t_q:=\frac{1}{i}[I&0 0&-I]\frac{d}{dx}+[0&q q^*&0] $$ and some separated boundary conditions. Here $q$ is an $r\times r$ matrix-valued function with entries belonging to $L_2((0,1),\mathbb C)$ and $I$ is the identity $r\times r$ matrix. We give a complete description of the spectral data (eigenvalues and suitably introduced norming matrices) for the operators under consideration and suggest an algorithm of reconstructing the potential $q$ from the corresponding spectral data.
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