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On the Partial Inverse Problems for the Transmission Eigenvalue Problem of the Schrödinger Operator

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Abstract

In this work, we study the partial inverse problems for the Schrödinger transmission eigenvalue problem. It is shown that if the potential is partially known a prior, then only partial eigenvalues can uniquely determine the potential. The relationship between the density of the known eigenvalues and the length of the subinterval on the given potential is revealed.

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Acknowledgements

The research work was supported in part by the National Natural Science Foundation of China (11901304) and the Startup Foundation for Introducing Talent of NUIST.

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  1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, Jiangsu, People’s Republic of China

    Qiao-Qiao Xu & Xiao-Chuan Xu

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  1. Qiao-Qiao Xu
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Correspondence to Xiao-Chuan Xu.

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Xu, QQ., Xu, XC. On the Partial Inverse Problems for the Transmission Eigenvalue Problem of the Schrödinger Operator. Results Math 76, 79 (2021). https://doi.org/10.1007/s00025-021-01395-5

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