TY - JOUR
AU - A. M. Gomilko
AU - V. N. Pivovarchik
PY - 2008/09/25
Y2 - 2024/07/24
TI - Inverse Sturm-Liouville problem on a figure-eight graph
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 60
IS - 9
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/3235
AB - 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.
ER -