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An interior inverse problem for the Sturm-Liouville operator with discontinuous conditions. (English) Zbl 1173.34306

Summary: We study the inverse problem for the Sturm-Liouville operator \(-D^{2}+q\) with discontinuity boundary conditions inside a finite closed interval. Using spectral data of a kind, it is shown that the potential function \(q(x)\) can be uniquely determined by a set of values of eigenfunctions at some internal point and one spectrum.

MSC:

34A55 Inverse problems involving ordinary differential equations
34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators
47E05 General theory of ordinary differential operators
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