On the reconstruction of a convolution perturbation of the Sturm-Liouville operator from the spectrum |
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Authors: | S A Buterin |
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Institution: | 1.Saratov State University,Saratov,Russia |
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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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Keywords: | |
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