An inverse problem for Sturm-Liouville operators on arbitrary compact spatial networks (Q610579)

The paper deals with the problem of the reconstruction of potentials of the Sturm-Liouville operator considered on a finite graph from a set of spectral data. This set consists of eigenvalues of boundary value problems with appropriately chosen boundary conditions and matching conditions (at the internal vertices of the graph). No restrictions are assumed on the graph structure, which distinguishes the present paper from previous works on the subject. The author proves the uniqueness theorem for the inverse problem and gives the reconstruction procedure.