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 Mat. Sb. (N.S.), 1988, Volume 137(179), Number 2(10), Pages 242–259 (Mi msb1785)

An inverse problem for a selfadjoint differential operator on the line

V. V. Sukhanov

Abstract: The inverse problem is considered for a high-order differential operator on the line. The inverse problem is formulated in terms of the Riemann problem. The data of the inverse problem arise as coefficients of the junction matrix of the Riemann problem. Under specific relations on the data of the inverse problem, which correspond to the self-adjointness of the original operator, the solvability of the Riemann problem is proved. The solution of the Riemann problem yields the solution of the inverse problem, as established in the paper.
Bibliography: 11 titles.

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English version:
Mathematics of the USSR-Sbornik, 1990, 65:1, 249–266

Bibliographic databases:

UDC: 517.95
MSC: Primary 31B20, 34B25; Secondary 30E25, 34E05, 45E05, 31A25, 47E05, 81F99

Citation: V. V. Sukhanov, “An inverse problem for a selfadjoint differential operator on the line”, Mat. Sb. (N.S.), 137(179):2(10) (1988), 242–259; Math. USSR-Sb., 65:1 (1990), 249–266

Citation in format AMSBIB
\Bibitem{Suk88} \by V.~V.~Sukhanov \paper An inverse problem for a~selfadjoint differential operator on the line \jour Mat. Sb. (N.S.) \yr 1988 \vol 137(179) \issue 2(10) \pages 242--259 \mathnet{http://mi.mathnet.ru/msb1785} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=971696} \zmath{https://zbmath.org/?q=an:0677.34013|0658.34010} \transl \jour Math. USSR-Sb. \yr 1990 \vol 65 \issue 1 \pages 249--266 \crossref{https://doi.org/10.1070/SM1990v065n01ABEH001144} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Iurko V., “Restoration of Differential-Operators From Weyl Matrix”, 313, no. 6, 1990, 1368–1372
2. V. A. Yurko, “Recovery of nonselfadjoint differential operators on the half-line from the Weyl matrix”, Math. USSR-Sb., 72:2 (1992), 413–438
3. Yurko V., “The Inverse Problem for Self-Adjoint Differential-Operators on the Half-Line”, Dokl. Akad. Nauk, 333:4 (1993), 449–451
4. V. A. Yurko, “On determination of self-adjoint differential operators on a semiaxis”, Math. Notes, 57:3 (1995), 310–318
5. Fritz Gesztesy, Eduard Tsekanovskii, “On Matrix-Valued Herglotz Functions”, Math Nachr, 218:1 (2000), 61
6. V. A. Yurko, “An inverse spectral problem for singular non-self-adjoint differential systems”, Sb. Math., 195:12 (2004), 1823–1854
7. A Laptev, R Shterenberg, V Sukhanov, J Östensson, “Reflectionless potentials for an ordinary differential operator of order four”, Inverse Probl, 22:1 (2006), 135
8. Badanin A. Korotyaev E.L., “Even Order Periodic Operators on the Real Line”, Int. Math. Res. Notices, 2012, no. 5, 1143–1194
9. R. G. Shterenberg, V. V. Sukhanov, “Scattering for differential operators of order four on the half-line. I. Direct problem”, St. Petersburg Math. J., 25:2 (2014), 327–337
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