We consider the inverse eigenvalue problems for stationary Dirac systems with differentiable self-adjoint matrix potential. The theorem of Ambarzumyan for a Sturm-Liouville problem is extended to Dirac operators, which are subject to separation boundary conditions or periodic (semi-periodic) boundary conditions, and some analogs of Ambarzumyan’s theorem are obtained. The proof is based on the existence and extremal properties of the smallest eigenvalue of corresponding vectorial Sturm-Liouville operators, which are the second power of Dirac operators.

中文翻译：

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Dirac算子的Ambarzumyan定理

我们考虑具有可微自伴矩阵势的平稳Dirac系统的特征值反问题。将Sturm-Liouville问题的Ambarzumyan定理扩展到Dirac算子，该算子要服从分离边界条件或周期（半周期）边界条件，并获得Ambarzumyan定理的一些类似物。该证明基于相应矢量Sturm-Liouville算子的最小特征值的存在和极值性质，这是Dirac算子的第二幂。