A partial inverse problem for the Sturm-Liouville operator on a star-shaped graph
Spectral Theory
2017-01-03 v1
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.
Cite
@article{arxiv.1701.00219,
title = {A partial inverse problem for the Sturm-Liouville operator on a star-shaped graph},
author = {Natalia Bondarenko},
journal= {arXiv preprint arXiv:1701.00219},
year = {2017}
}