# Inverse Sturm-Liouville problem on a figure-eight graph

### Abstract

We study the inverse problem for the Strum-Liouville equation on a graph that consists of two quasione-dimensional loops of the same length having a common vertex. As spectral data, we consider the set of eigenvalues of the entire system together with the sets of eigenvalues of two Dirichlet problems for the Sturm-Liouville equations with the condition of total reflection at the vertex of the graph. We obtain conditions for three sequences of real numbers that enable one to reconstruct a pair of real potentials from L 2 corresponding to each loop. We give an algorithm for the construction of the entire set of potentials corresponding to this triple of spectra.
Published

25.09.2008

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 60, no. 9, Sept. 2008, pp. 1168–1188, https://umj.imath.kiev.ua/index.php/umj/article/view/3235.

Issue

Section

Research articles