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Ambarzumyan Theorems for Dirac Operators

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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.

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Correspondence to Chuan-fu Yang.

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The research work was supported in part by the National Natural Science Foundation of China (11871031) and by the Natural Science Foundation of the Jiangsu Province of China (BK 20201303).

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Yang, Cf., Wang, F. & Huang, Zy. Ambarzumyan Theorems for Dirac Operators. Acta Math. Appl. Sin. Engl. Ser. 37, 287–298 (2021).

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2000 MR Subject Classification