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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Translated from Matematicheskie Zametki, vol. 80, no. 5, 2006, pp. 668–682.
Original Russian Text Copyright © 2006 by S. A. Buterin.
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Buterin, S.A. Inverse spectral reconstruction problem for the convolution operator perturbed by a one-dimensional operator. Math Notes 80, 631–644 (2006). https://doi.org/10.1007/s11006-006-0184-6
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DOI: https://doi.org/10.1007/s11006-006-0184-6