Geodesic
Inverse Problems for Differential Operators of Any Order on Trees
Matematičeskie zametki, Tome 83 (2008) no. 1, pp. 139-152 Cet article a éte moissonné depuis la source Math-Net.Ru

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Inverse spectral problems for ordinary differential operators of any order on compact trees are studied. As the main spectral characteristics, Weyl matrices, which generalize the Weyl $m$-function for the classical Sturm–Liouville operator are introduced and studied. A constructive solution procedure for the inverse problem based on Weyl matrices is suggested, and the uniqueness of the solution is proved. The reconstruction of differential equations from discrete spectral characteristics is also considered.
Keywords: differential operator on a tree, inverse spectral problem on a tree, method of spectral mappings.
Mots-clés : Weyl solution, Weyl matrix 
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V. A. Yurko. Inverse Problems for Differential Operators of Any Order on Trees. Matematičeskie zametki, Tome 83 (2008) no. 1, pp. 139-152. http://geodesic.mathdoc.fr/item/MZM_2008_83_1_a14/

[1] Yu. V. Pokornyi, O. M. Penkin, V. L. Pryadiev, A. V. Borovskikh, K. P. Lazarev, S. A. Shabrov, Differentsialnye uravneniya na geometricheskikh grafakh, Fizmatlit, M., 2004 | MR | Zbl

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

[3] V. A. Marchenko, Operatory Shturma–Liuvillya i ikh prilozheniya, Naukova Dumka, Kiev, 1977 | MR | Zbl

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

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

[6] A. L. Bukhgeim, Introduction to the Theory of Inverse Problems, Inverse Ill-posed Probl. Ser., VSP, Utrecht, 2000

[7] A. M. Denisov, Elements of the theory of inverse problems, Inverse Ill-posed Probl. Ser., VSP, Utrecht, 1999 | MR | Zbl

[8] S. I. Kabanikhin, A. D. Satybaev, M. A. Shishlenin, Direct Methods of Solving Multi-dimensional Inverse Hyperbolic Problems, Inverse Ill-posed Probl. Ser., VSP, Utrecht, 2005 | MR | Zbl

[9] M. M. Lavrentiev, A. V. Avdeev, M. M. Lavrentiev Jr., V. I. Priimenko, Inverse Problems of Mathematical Physics, Inverse Ill-posed Probl. Ser., VSP, Utrecht, 2003 | MR | Zbl

[10] A. I. Prilepko, D. G. Orlovsky, I. A. Vasin, Methods for Solving Inverse Problems in Mathematical Physics, Monogr. Textbooks Pure Appl. Math., 231, Marcel Dekker, New York, 2000 | MR | Zbl

[11] V. G. Romanov, Obratnye zadachi matematicheskoi fiziki, Nauka, M., 1984 | MR | Zbl

[12] M. A. Naimark, Lineinye differentsialnye operatory, Nauka, M., 1969 | MR | Zbl | Zbl