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Inverse problem for interior spectral data of the Dirac operator on a finite interval. (English) Zbl 1021.34073
The authors consider the Dirac operator, generated by the differential expression $$ l(y)=By'+Qy, \quad 0\leq x\leq 1, $$ with $$ B=\pmatrix 0 & 1 \cr -1 & 0 \endpmatrix, \quad Q(x)=\pmatrix p(x) & q(x) \cr q(x) & -p(x)\endpmatrix, \quad y(x)=\pmatrix y_1(x) \cr y_2(x)\endpmatrix,$$ 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.

MSC:
34L40Particular ordinary differential operators
34B24Sturm-Liouville theory
34L05General spectral theory for OD operators
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References:
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