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Ambarzumyan’s Theorem for the Dirac Operator on Equilateral Tree Graphs

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Abstract

The classical Ambarzumyan’s theorem states that if the Neumann eigenvalues of the Sturm-Liouville operator \( - {{{d^2}} \over {d{x^2}}} + q\) with an integrable real-valued potential q on [0, π] are {n2: n ≥ 0}, then q = 0 for almost all x ∈ [0, π]. In this work, the classical Ambarzumyan’s theorem is extended to the Dirac operator on equilateral tree graphs. We prove that if the spectrum of the Dirac operator on graphs coincides with the unperturbed case, then the potential is identically zero.

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Authors and Affiliations

  1. Department of Mathematics, School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing, 210094, China

    Dong-Jie Wu, Xin-Jian Xu & Chuan-Fu Yang

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  1. Dong-Jie Wu
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  2. Xin-Jian Xu
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  3. Chuan-Fu Yang
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Correspondence to Chuan-Fu Yang.

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The authors declare no conflict of interest.

Additional information

The project is supported by the National Natural Science Foundation of China (No. 11871031) and the Natural Science Foundation of the Jiangsu Province of China (No. BK 20201303).

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Wu, DJ., Xu, XJ. & Yang, CF. Ambarzumyan’s Theorem for the Dirac Operator on Equilateral Tree Graphs. Acta Math. Appl. Sin. Engl. Ser. 40, 568–576 (2024). https://doi.org/10.1007/s10255-024-1042-6

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  • DOI: https://doi.org/10.1007/s10255-024-1042-6

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