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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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