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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Inverse spectral problem with partial information given on the potential and norming constants


Authors: Guangsheng Wei and Hong-Kun Xu
Journal: Trans. Amer. Math. Soc. 364 (2012), 3265-3288
MSC (2010): Primary 34A55; Secondary 34L40, 34L20
Published electronically: November 7, 2011
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05545-5
PII: S 0002-9947(2011)05545-5
Keywords: Eigenvalue, norming constant, boundary condition, inverse spectral problem
Received by editor(s): August 9, 2010
Received by editor(s) in revised form: January 15, 2011
Published electronically: November 7, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.