Reconstruction of Sturm-Liouville differential operators on A-graphs (Q542155)

The paper presents a study of the inverse spectral problem for Sturm-Liouville differential operators defined on graphs. It turns out that inverse problems for graphs with cycles are more difficult to investigate. In previous papers by the author, the inverse problem was solved in the case of graphs with one cycle only. The present paper deals with the more general situation where arbitrarily many cycles are admitted, under the assumption that the graph belongs to the class of \(A\)-graphs. The latter means that two arbitrary cycles cannot have more than one common point. The author gives the formulation of the inverse problem on such graphs with standard matching conditions at the internal vertices, studies the properties of spectra, characteristic functions and Weyl functions, proves the uniqueness theorem for the solution of the inverse problem and presents a constructive solution to it.