Inverse spectral problem with partial information given on the potential and norming constants
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Abstract:
The inverse spectral problem for a Sturm-Liouville equation in Liouville form with separated self-adjoint boundary conditions on the unit interval $[0,1]$ is considered. Some uniqueness results are obtained which imply that the potential $q$ can be completely determined even if only partial information is given on $q$ 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 problem of missing eigenvalues and norming constants is also investigated in the situation where the potential $q$ is $C^{2k-1}$ and the boundary conditions at the endpoints $0$ and $1$ are fixed.References
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Additional Information
- Guangsheng Wei
- Affiliation: College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, People’s Republic of China
- Email: weimath@vip.sina.com
- Hong-Kun Xu
- Affiliation: Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
- Email: xuhk@math.nsysu.edu.tw
- Received by editor(s): August 9, 2010
- Received by editor(s) in revised form: January 15, 2011
- Published electronically: November 7, 2011
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 3265-3288
- MSC (2010): Primary 34A55; Secondary 34L40, 34L20
- DOI: https://doi.org/10.1090/S0002-9947-2011-05545-5
- MathSciNet review: 2888245