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

By Natalia Pavlovna Bondarenko. 2017

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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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/26022eeafd633bbd12204085963aed40ebd89182