Geodesic
On the solvability of the inverse Sturm--Liouville problem in the central symmetry case
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 8 (2008) no. 1, pp. 21-24.

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Necessary and sufficient conditions are provided for the solvability of the inverse problem of recovering Sturm–Liouville operator from its spectrum in the central symmetry case. 
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T. V. Mazur. On the solvability of the inverse Sturm--Liouville problem in the central symmetry case. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 8 (2008) no. 1, pp. 21-24. http://geodesic.mathdoc.fr/item/ISU_2008_8_1_a3/

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