Geodesic
Uniqueness of the solution of the inverse problem for differential operators on arbitrary compact graphs
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 3, pp. 33-38 
V. A. Yurko. Uniqueness of the solution of the inverse problem for differential operators on arbitrary compact graphs. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 3, pp. 33-38. http://geodesic.mathdoc.fr/item/ISU_2010_10_3_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

An inverse spectral problem is studied for Sturm–Liouville operators on arbitrary compact graphs with standard matching conditions in internal vertices. A uniqueness theorem of recovering operator's coefficients from spectra is proved.

[1] Belishev M. I., “Boundary spectral inverse problem on a class of graphs (trees) by the BC method”, Inverse Problems, 20 (2004), 647–672 | DOI | MR | Zbl

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

[3] Brown B. M., Weikard R., “A Borg–Levinson theorem for trees”, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 461:2062 (2005), 3231–3243 | DOI | MR | Zbl

[4] Freiling G., Yurko V. A, “Inverse spectral problems for Sturm–Liouville operators on noncompact trees”, Results in Mathematics, 50 (2007), 195–212 | DOI | MR

[5] Yurko V. A., “Recovering differential pencils on compact graphs”, J. Diff. Equations, 244 (2008), 431–443 | DOI | MR | Zbl

[6] Yurko V. A., “Obratnye zadachi dlya differentsialnykh operatorov proizvolnykh poryadkov na derevyakh”, Mat. zametki, 83:1 (2008), 139–152 | DOI | MR | Zbl

[7] Yurko V. A., “Obratnaya spektralnaya zadacha dlya puchkov differentsialnykh operatorov na nekompaktnykh prostranstvennykh setyakh”, Differentsialnye uravneniya, 44:12 (2008), 1658–1666 | MR

[8] Yurko V. A., “Inverse problems for Sturm–Liouville operators on bush-type graphs”, Inverse Problems, 25:10 (2009), 105008 | DOI | MR | Zbl

[9] Yurko V. A., “Ob obratnoi spektralnoi zadache dlya differentsialnykh operatorov na grafe-ezhe”, Dokl. RAN, 425:4 (2009), 466–470 | MR | Zbl

[10] Marchenko V. A., Operatory Shturma–Liuvillya i ikh prilozheniya, Nauk. dumka, Kiev, 1977, 331 pp. | MR

[11] Levitan B. M., Obratnye zadachi Shturma–Liuvillya, Nauka, M., 1984, 240 pp. | MR | Zbl

[12] Freiling G., Yurko V. A., Inverse Sturm–Liouville Problems and their Applications, NOVA Science Publishers, N.Y., 2001, 305 pp. | MR | Zbl

[13] Yurko V. A., Method of Spectral Mappings in the Inverse Problem Theory, Inverse and Ill-posed Problems Series, VSP, Utrecht, 2002, 303 pp. | MR | Zbl

[14] Beals R., Deift P., Tomei C., Direct and Inverse Scattering on the Line, Math. Surveys and Monographs, 28, Amer. Math. Soc., Providence, R.I., 1988, 275 pp. | DOI | MR | Zbl

[15] Yurko V. A., Inverse Spectral Problems for Differential Operators and their Applications, Gordon and Breach, Amsterdam, 2000, 253 pp. | MR | Zbl

[16] Yurko V. A., Vvedenie v teoriyu obratnykh spektralnykh zadach, Fizmatlit, M., 2007, 384 pp. | Zbl

[17] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969, 526 pp. | MR | Zbl

[18] Bellmann R., Cooke K., Differential-difference Equations, Academic Press, N.Y., 1963, 548 pp. | MR

[19] Conway J. B., Functions of One Complex Variable, 2nd ed., Springer-Verlag, N.Y., 1995, 445 pp. | MR | Zbl