Abstract
Under study is the inverse spectral problem for a Sturm-Liouville operator in impedance form. We prove that the discontinuities of the impedance are uniquely determined by the asymptotics of the Jost function at infinity. Some algorithm is constructed that makes it possible to recover the discontinuities of the impedance.
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The author was supported by the Russian Foundation for Basic Research (Grants 12-01-00390 and 14-01-31165), the Presidium of the Russian Academy of Sciences (Program of Fundamental Research No. 15, Project 121), and the Siberian Division of the Russian Academy of Sciences (Interdisciplinary Integration Project 30).
Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 2, pp. 455–462, March–April, 2015.
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Sedipkov, A.A. Recovery of the discontinuities of the coefficient of a Sturm-Liouville operator in impedance form. Sib Math J 56, 367–372 (2015). https://doi.org/10.1134/S0037446615020160
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DOI: https://doi.org/10.1134/S0037446615020160