A 2-edge partial inverse problem for the Sturm-Liouville operators with singular potentials on a star-shaped graph
Spectral Theory
2017-02-28 v1
Abstract
Boundary value problems for Sturm-Liouville operators with potentials from the class on a star-shaped graph are considered. We assume that the potentials are known on all the edges of the graph except two, and show that the potentials on the remaining edges can be constructed by fractional parts of two spectra. A uniqueness theorem is proved, and an algorithm for the constructive solution of the partial inverse problem is provided. The main ingredient of the proofs is the Riesz-basis property of specially constructed systems of functions.
Keywords
Cite
@article{arxiv.1702.08293,
title = {A 2-edge partial inverse problem for the Sturm-Liouville operators with singular potentials on a star-shaped graph},
author = {Natalia P. Bondarenko},
journal= {arXiv preprint arXiv:1702.08293},
year = {2017}
}