Geodesic
Necessary and sufficient conditions for the solvability of the inverse problem for Sturm–Liouville operators with a nonintegrable singularity inside a finite interval
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 3, pp. 59-64 
A. E. Fedoseev. Necessary and sufficient conditions for the solvability of the inverse problem for Sturm–Liouville operators with a nonintegrable singularity inside a finite interval. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 3, pp. 59-64. http://geodesic.mathdoc.fr/item/ISU_2013_13_3_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The inverse spectral problem of recovering Sturm–Liouville operators on a finite interval with a nonintegrable Bessel-type singularity in an interior point from the given spectral data is studied. A corresponding uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided. Necessary and sufficient conditions for the solvability of the inverse problem are obtained.

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