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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:
34A55Inverse problems of ODE
34L20Asymptotic distribution of eigenvalues for OD operators
47E05Ordinary differential operators
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