Solution of a model inverse spectral problem for the Sturm–Liouville operator on a graph

N. F. Valeev^a, Yu. V. Martynova^b, Ya. T. Sultanaev<sup>c

a</sup> Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa
^b RN-UfaNIPIneft Company
^c Bashkir State Pedagogical University, Ufa

Abstract: A model inverse spectral problem for the Sturm–Liouville operator on a geometric graph is studied. This problem consists in finding $N$ parameters of the boundary conditions using its $N$ known eigenvalues. It is shown that the problem under consideration possess the property of a monotonic dependence of its eigenvalues on the parameters of the boundary conditions. This problem is reduced to a multiparameter inverse spectral problem for the operator in a finite-dimensional space. A new algorithm for the numerical solution of this problem is proposed.

Keywords: spectral theory of differential operators, geometric graph, Sturm–Liouville operator, spectral problems.

UDC: 517.4+519.71

Received: 17.05.2016