A partial inverse Sturm‐Liouville problem on an arbitrary graphстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 6 октября 2021 г.
Аннотация:The Sturm-Liouville operator with singular potentials of class W_2^{-1} on a graph of arbitrary geometrical structure is considered. We study the partial inverse problem, which consists in the recovery of the potential on a boundary edge of the graph from a subspectrum under the assumption that the potentials on the other edges are known a priori. We obtain (i) the uniqueness theorem, (ii) a reconstruction algorithm, (iii) global solvability, and (iv) local solvability and stability for this inverse problem. Our method is based on reduction of the partial inverse problem on a graph to the Sturm-Liouville problem on a finite interval with entire analytic functions in the boundary condition.