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.

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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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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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