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ISSN 1088-6850(e) ISSN 0002-9947(p)

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
Posted: 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 is considered. Some uniqueness results are obtained which imply that the potential can be completely determined even if only partial information is given on 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 is $C^{2k-1}$ and the boundary conditions at the endpoints 0 and are fixed.

References

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