On the uniqueness of the solution of the inverse Sturm-Liouville problem with nonseparated boundary conditions on a geometric graph (Q1994087)

The classical Sturm-Liouville equation is considered on a star-shaped graph with three edges and with boundary conditions at the boundary edges. The authors study an inverse problem of recovering coefficients in the boundary conditions from the given eigenvalues, provided that coefficients in the differential equations (potentials) are known a priori. Uniqueness results are obtained for this class of inverse problems.