Geodesic
Inverse problem for Sturm--Liouville operator on the half-line having nonintegrable singularity in an interior point
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 4, pp. 49-55.

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The inverse problem of recovering Sturm–Liouville operators on the half-line with a nonintegrable Bessel-type singularity in an interior point from the given Weyl function is studied. The corresponding uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided. Necessary and sufficient conditions of the solvability of the inverse problem are obtained. 
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A. E. Fedoseev. Inverse problem for Sturm--Liouville operator on the half-line having nonintegrable singularity in an interior point. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 4, pp. 49-55. http://geodesic.mathdoc.fr/item/ISU_2012_12_4_a8/

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