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The uniqueness of inverse problem for the Dirac operators with partial information

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Abstract

The inverse spectral problem for the Dirac operators defined on the interval [0, π] with self-adjoint separated boundary conditions is considered. Some uniqueness results are obtained, which imply that the pair of potentials (p(x), r(x)) and a boundary condition are uniquely determined even if only partial information is given on (p(x), r(x)) together with partial information on the spectral data, consisting of either one full spectrum and a subset of norming constants, or a subset of pairs of eigenvalues and the corresponding norming constants. Moreover, the authors are also concerned with the situation where both p(x) and r(x) are C n-smoothness at some given point.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, China

    Zhaoying Wei & Guangsheng Wei

  2. College of Science, Xi’an Shiyou University, Xi’an, 710065, China

    Zhaoying Wei

Authors
  1. Zhaoying Wei
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  2. Guangsheng Wei
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Correspondence to Zhaoying Wei.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 11171198) and the Scientific Research Program Funded by Shaanxi Provincial Education Department (No. 2013JK0563).

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Wei, Z., Wei, G. The uniqueness of inverse problem for the Dirac operators with partial information. Chin. Ann. Math. Ser. B 36, 253–266 (2015). https://doi.org/10.1007/s11401-015-0885-9

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  • DOI: https://doi.org/10.1007/s11401-015-0885-9

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