Inverse Sturm-Liouville problem on a figure-eight graph
AbstractWe 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.
How to Cite
Gomilko, A. M., and V. N. Pivovarchik. “Inverse Sturm-Liouville Problem on a Figure-Eight Graph”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, no. 9, Sept. 2008, pp. 1168–1188, https://umj.imath.kiev.ua/index.php/umj/article/view/3235.