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 Izv. Saratov Univ. Math. Mech. Inform., 2017, Volume 17, Issue 3, Pages 276–284 (Mi isu723)

Scientific Part
Mathematics

On recovering integro-differential operators from the Weyl function

M. Yu. Ignatiev, S. Yu. Sovetnikova

Saratov State University, Astrakhanskaya Str., 83, Saratov, Russia, 410012

Abstract: We study inverse problems of spectral analysis for second order integro-differential operators, which are a perturbation of the Sturm–Liouville operator by the integral Volterra operator. We pay the main attention to the nonlinear inverse problem of recovering the potential from the given Weyl function provided that the kernel of the integral operator is known a priori. We obtain properties of the spectral characteristics and the Weyl function, provide an algorithm for constructing the solution of the inverse problem and establish the uniqueness of the solution. For solving the inverse problem we use the method of standard models.

Key words: integro-differential operators, inverse spectral problems, uniqueness result, algorithm.

 Funding Agency Grant Number Russian Science Foundation 17-11-01193 This work was supported by the Russian Science Foundation (project no. 17-11-01193).

DOI: https://doi.org/10.18500/1816-9791-2017-17-3-276-284

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UDC: 517.984

Citation: M. Yu. Ignatiev, S. Yu. Sovetnikova, “On recovering integro-differential operators from the Weyl function”, Izv. Saratov Univ. Math. Mech. Inform., 17:3 (2017), 276–284

Citation in format AMSBIB
\Bibitem{IgnSov17} \by M.~Yu.~Ignatiev, S.~Yu.~Sovetnikova \paper On recovering integro-differential operators from the Weyl function \jour Izv. Saratov Univ. Math. Mech. Inform. \yr 2017 \vol 17 \issue 3 \pages 276--284 \mathnet{http://mi.mathnet.ru/isu723} \crossref{https://doi.org/10.18500/1816-9791-2017-17-3-276-284} \elib{https://elibrary.ru/item.asp?id=29897300}