@article{Gomilko_Pivovarchik_2008, title={Inverse Sturm-Liouville problem on a figure-eight graph}, volume={60}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/3235}, abstractNote={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.}, number={9}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Gomilko, A. M. and Pivovarchik, V. N.}, year={2008}, month={Sep.}, pages={1168–1188} }