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On theintegral equation of the first kind reduction to the equation with a degenerate kernel

An abstract ill-posed inverse problem reduced to the integral Fredgholm equation of the first kind is considered. The paper is devoted to the semi-heuristic scheme of the apriori predictions destined for the analysis of the reconstruction possibilities from the given level of the initial data errors. The upper bounds are derived which admit, in the case of the appropriate relation between the parameters, to carry out the pre-dictions using the degenerate approximation for the kernel of the integral operator.

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