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A partial inverse problem for the Sturm-Liouville operator on a star-shaped graph

The Sturm-Liouville operator on a star-shaped graph is considered. We assume that the potential is known a priori on all the edges except one, and study the partial inverse problem, which consists in recovering the potential on the remaining edge from the part of the spectrum. A constructive method is developed for the solution of this problem, based on the Riesz-basicity of some sequence of vector functions. The local solvability of the inverse problem and the stability of its solution are proved.

preprint2017arXivOpen access
Natalia Bondarenko
math.SP
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Natalia Bondarenko

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