Inverse Sturm-Liouville problem on a figure-eight graph
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.
English version (Springer): Ukrainian Mathematical Journal 60 (2008), no. 9, pp 1360-1385.
Citation Example: Gomilko A. M., Pivovarchik V. N. Inverse Sturm-Liouville problem on a figure-eight graph // Ukr. Mat. Zh. - 2008. - 60, № 9. - pp. 1168–1188.