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On the reconstruction of a convolution perturbation of the Sturm-Liouville operator from the spectrum

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Abstract

We consider the sum of the Sturm-Liouville operator and a convolution operator. We study the inverse problem of reconstructing the convolution operator from the spectrum. This problem is reduced to a nonlinear integral equation with a singularity. We prove the global solvability of this nonlinear equation, which permits one to show that the asymptotics of the spectrum is a necessary and sufficient condition for the solvability of the inverse problem. The proof is constructive.

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Authors and Affiliations

  1. Saratov State University, Saratov, Russia

    S. A. Buterin

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  1. S. A. Buterin
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Original Russian Text © S.A. Buterin, 2010, published in Differentsial’nye Uravneniya, 2010, Vol. 46, No. 1, pp. 146–149.

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Buterin, S.A. On the reconstruction of a convolution perturbation of the Sturm-Liouville operator from the spectrum. Diff Equat 46, 150–154 (2010). https://doi.org/10.1134/S0012266110010167

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  • DOI: https://doi.org/10.1134/S0012266110010167

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