Geodesic
Recovering differential operators on a graph with a cycle and with generalized matching conditions
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 8 (2008) no. 3, pp. 10-17 
V. A. Yurko. Recovering differential operators on a graph with a cycle and with generalized matching conditions. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 8 (2008) no. 3, pp. 10-17. http://geodesic.mathdoc.fr/item/ISU_2008_8_3_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The solution of the inverse spectral problem is obtained for second-order differential operators on a graph with a cycle and with generalized matching conditions in the internal vertex.

[1] Marchenko V. A., Operatory Shturma–Liuvillya i ikh prilozheniya, Nauk. dumka, Kiev, 1977 | MR

[2] Levitan B. M., Obratnye zadachi Shturma–Liuvillya, Nauka, M., 1984 | MR

[3] Beals R., Deift P., Tomei C., Direct and Inverse Scattering on the Line, Math. Surveys and Monographs, 28, Amer. Math. Soc., Providence: RI, 1988 | DOI | MR | Zbl

[4] Freiling G., Yurko V. A., Inverse Sturm–Liouville Problems and their Applications, NOVA Science Publishers, N.Y., 2001 | MR | Zbl

[5] Yurko V. A., Method of Spectral Mappings in the Inverse Problem Theory, Inverse and Ill-posed Problems Series, VSP, Utrecht, 2002 | MR | Zbl

[6] Yurko V. A., Vvedenie v teoriyu obratnykh spektralnykh zadach, Fizmatlit, M., 2007 | Zbl

[7] Pokornyi Yu. V., Penkin O. M., Pryadiev V. L. i dr., Differentsialnye uravneniya na geometricheskikh grafakh, Fizmatlit, M., 2004 | Zbl

[8] Yurko V. A., “Inverse spectral problems for Sturm–Liouville operators on graphs”, Inverse Problems, 21 (2005), 1075–1086 | DOI | MR | Zbl

[9] Naimark M. A., Linear Differential Operators, 2nd ed., Nauka, M., 1969 ; English transl. of 1st ed. v. I, II, Ungar, N.Y., 1967 ; 1968 | MR | Zbl | Zbl | Zbl

[10] Bellmann R., Cooke K., Differential-difference Equations, Academic Press, N.Y., 1963 | MR

[11] Conway J. B., Functions of One Complex Variable, v. I, 2nd ed., Springer-Verlag, N.Y., 1995 | MR | Zbl

[12] Stankevich I. V., “Ob odnoi obratnoi zadache spektralnogo analiza dlya uravneniya Khilla”, Dokl. AN SSSR, 192:1 (1970), 34–37

[13] Marchenko V. A., Ostrovskii I. V., “Kharakteristika spektra operatora Khilla”, Mat. sb., 97:4 (1975), 540–606 | MR | Zbl