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. 
@article{MZM_2006_79_4_a13,
     author = {V. A. Yurko},
     title = {On recovering {Sturm--Liouville} operators on graphs},
     journal = {Matemati\v{c}eskie zametki},
     pages = {619--630},
     publisher = {mathdoc},
     volume = {79},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_4_a13/}
}
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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/