Inverse spectral reconstruction problem for the convolution operator perturbed by a one-dimensional operator |
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Authors: | S. A. Buterin |
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Affiliation: | (1) N. G. Chernyshevskii Saratov State University, Russia |
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Abstract: | We consider a one-dimensional perturbation of the convolution operator. We study the inverse reconstruction problem for the convolution component using the characteristic numbers under the assumption that the perturbation summand is known a priori. The problem is reduced to the solution of the so-called basic nonlinear integral equation with singularity. We prove the global solvability of this nonlinear equation. On the basis of these results, we prove a uniqueness theorem and obtain necessary and sufficient conditions for the solvability of the inverse problem. |
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Keywords: | inverse spectral reconstruction problem convolution operator nonlinear integral equation Fredholm alternative Hilbert-Schmidt operator |
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