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Uniqueness results for inverse Sturm-Liouville problems with partial information given on the potential and spectral data

Research paper by Zhaoying Wei, Guangsheng Wei

Indexed on: 11 Nov '16Published on: 11 Nov '16Published in: Boundary Value Problems



Abstract

We consider the inverse spectral problem for a Sturm-Liouville problem on the unit interval \([0,1]\). We obtain some uniqueness results, 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 the spectrum and normalizing constants. Moveover, we also investigate the problem of missing both eigenvalues and normalizing constants in the situation where the potential q is \(C^{2k-1}\) near a suitable point.