Geodesic
Inverse spectral problem of reconstructing one-dimensional perturbation of integral Volterra operator
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 6 (2006) no. 1, pp. 3-11

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An integral operator representable as the sum of a Volterra operator and one-dimensional one is considered, when the inverse operator for Volterra one is an integro-differential operator of second order. The inverse problem of reconstruction of the one-dimensional item from spectral data provided that the Volterra component is known a priori is investigated. The uniqueness of the solution of the inverse problem is proved and conditions are obtained that are necessary and sufficient for its solvability. 
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     title = {Inverse spectral problem of reconstructing one-dimensional perturbation of integral {Volterra} operator},
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S. A. Buterin. Inverse spectral problem of reconstructing one-dimensional perturbation of integral Volterra operator. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 6 (2006) no. 1, pp. 3-11. http://geodesic.mathdoc.fr/item/ISU_2006_6_1_a0/