Geodesic
On the scattering inverse problem for the differential operators of high order on the semi-axis
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (1989), pp. 26-32 
S. V. Babasian. On the scattering inverse problem for the differential operators of high order on the semi-axis. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (1989), pp. 26-32. http://geodesic.mathdoc.fr/item/UZERU_1989_3_a4/
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     author = {S. V. Babasian},
     title = {On the scattering inverse problem for the differential operators of high order on the semi-axis},
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     year = {1989},
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     url = {http://geodesic.mathdoc.fr/item/UZERU_1989_3_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

On semi-axis $(0, \infty)$ the self-adjoint differential operator of even order $2n>2$ is considered with the coefficients, convergent to the finite limit at the infinity. In conditions, providing the existence of the transform operator, the scattering data of $L$ operator are introduced, which are some of its spectral characteristics. Scattering inverse problem is raised, requiring the restoration of $L$ according to its scattering data. Solving the linear integral equation on the kernel of the transform operator an effective method for restoration of $L$ by the scattering data is developed. The uniqueness of such restoration is proved.

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