Inverse problem for interior spectral data of the Dirac operator on a finite interval
The authors consider the Dirac operator, generated by the differential expression \[ l(y)=By'+Qy, \quad 0\leq x\leq 1, \] with \[ B=\begin{pmatrix} 0 & 1 \cr -1 & 0 \end{pmatrix}, \quad Q(x)=\begin{pmatrix} p(x) & q(x) \cr q(x) & -p(x)\end{pmatrix}, \quad y(x)=\begin{pmatrix} y_1(x) \cr y_2(x)\end{pmatrix}, \] subject to the boundary conditions \[ y_1(0)\cos\alpha+y_2(0)\sin\alpha=0,\quad \alpha \in[0,\pi),\quad y_1(1)\cos\beta+y_2(1)\sin\beta=0,\quad \beta\in[0,\pi). \] The authors prove uniqueness theorems taking the spectrum and the set of values of the eigenfunctions at some interior point as the given data.
scientific article; zbMATH DE number 1833281