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

Natalia Bondarenko

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arXiv · 1701.00219

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

Natalia Bondarenko

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Abstract

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.

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BibTeX RIS

Natalia Bondarenko. 2017-01-01. A partial inverse problem for the Sturm-Liouville operator on a star-shaped graph. https://arxiv.org/abs/1701.00219

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