Geodesic
On recovering Sturm--Liouville operators on graphs
Matematičeskie zametki, Tome 79 (2006) no. 4, pp. 619-630.

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Sturm–Liouville differential operators on compact graphs are studied. We establish properties of the spectral characteristics and investigate three inverse problems of recovering the operator from the so-called Weyl functions, from discrete spectral data, and from a system of spectra. For these inverse problems, we prove uniqueness theorems and obtain procedures for constructing the solutions by the method of spectral mappings. 
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V. A. Yurko. On recovering Sturm--Liouville operators on graphs. Matematičeskie zametki, Tome 79 (2006) no. 4, pp. 619-630. http://geodesic.mathdoc.fr/item/MZM_2006_79_4_a13/

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