Geodesic
Solution of a class of inverse boundary-value Sturm--Liouville problems
Sbornik. Mathematics, Tome 186 (1995) no. 5, pp. 661-674

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A complete solution of a class of inverse problems in spectral analysis for the Sturm–Liouville operator is presented. That is, a) necessary and sufficient conditions are found for two sequences of real numbers to be spectra of boundary-value problems generated on a finite interval by a Sturm–Liouville equation and certain non-separated self-conjugate boundary conditions. A procedure for recovery of all such problems is given; b) additional spectral characteristics are found which together with the spectra uniquely define the Sturm–Liouville operator. 
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     author = {I. M. Guseinov and I. M. Nabiev},
     title = {Solution of a class of inverse boundary-value {Sturm--Liouville} problems},
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     number = {5},
     year = {1995},
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     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_5_a1/}
}
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I. M. Guseinov; I. M. Nabiev. Solution of a class of inverse boundary-value Sturm--Liouville problems. Sbornik. Mathematics, Tome 186 (1995) no. 5, pp. 661-674. http://geodesic.mathdoc.fr/item/SM_1995_186_5_a1/