Geodesic
On inverse periodic problem for differential operators for central symmetric potentials
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 1, pp. 68-75

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An inverse spectral problem for Sturm–Liouville operators on a finite interval with periodic boundary conditions is studied in the central symmetric case, when the potential is symmetric with respect to the middle of the interval. We discuss the statement of the problem, provide an algorithm for its solution along with necessary and sufficient conditions for the solvability of this nonlinear inverse problem. 
@article{ISU_2016_16_1_a5,
     author = {V. A. Yurko},
     title = {On inverse periodic problem for differential operators for central symmetric potentials},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {68--75},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2016_16_1_a5/}
}
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V. A. Yurko. On inverse periodic problem for differential operators for central symmetric potentials. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 1, pp. 68-75. http://geodesic.mathdoc.fr/item/ISU_2016_16_1_a5/