Geodesic
Inverse problem for the Sturm--Liouville operator with a frozen argument on the time scale
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1, Tome 208 (2022), pp. 49-62

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In this paper, we consider the problem of constructing the potential of the Sturm–Liouville equation with a frozen argument on the time scale by the spectrum of the Dirichlet boundary-value problem, where the time scale consists of two segments and the argument is frozen at the end of the first segment. We obtain the uniqueness theorem and construct an algorithm for solving the inverse problem together with necessary and sufficient conditions for its solvability. The case considered substantially differs from the case of the classical Sturm– Liouville operator with a frozen argument.
Keywords: inverse spectral problem, frozen argument, Sturm—Liouville operator, closed set.
Mots-clés : time scale 
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     author = {M. A. Kuznetsova},
     title = {Inverse problem for the {Sturm--Liouville} operator with a frozen argument on the time scale},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {49--62},
     publisher = {mathdoc},
     volume = {208},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_208_a6/}
}
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M. A. Kuznetsova. Inverse problem for the Sturm--Liouville operator with a frozen argument on the time scale. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1, Tome 208 (2022), pp. 49-62. http://geodesic.mathdoc.fr/item/INTO_2022_208_a6/