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Inverse Spectral Analysis for Regge Problem with Partial Information on the Potential

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Abstract

For the Regge problem, which can be characterized by a Sturm–Liouville problem with a Dirichlet boundary condition and an eigenparameter dependent boundary condition, it is known that the potential can be uniquely determined by all eigenvalues. In this paper, we prove that if the potential is known a prior on a subinterval of the whole interval, then infinitely many eigenvalues can be missing for the recovery of the potential. That is, the fraction of all eigenvalues can uniquely determine the potential on the whole interval. Moreover, the relationship between the proportion of the missing eigenvalues and the length of the subinterval on the given potential is revealed.

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Authors and Affiliations

  1. Department of Applied Mathematics, School of Science, Nanjing University of Science and Technology, Nanjing, 210094, Jiangsu, People’s Republic of China

    Xiao-Chuan Xu, Chuan-Fu Yang & Huang-Zhen You

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  1. Xiao-Chuan Xu
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  2. Chuan-Fu Yang
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  3. Huang-Zhen You
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Correspondence to Xiao-Chuan Xu.

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Xu, XC., Yang, CF. & You, HZ. Inverse Spectral Analysis for Regge Problem with Partial Information on the Potential. Results Math 71, 983–996 (2017). https://doi.org/10.1007/s00025-015-0523-6

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  • DOI: https://doi.org/10.1007/s00025-015-0523-6

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