Recovering of the stiffness coefficients of the Sturm-Liouville operator on a star graph from a finite set of its eigenvalues (Q6649014)

The paper deals with the Sturm-Liouville operator on the star-shaped graph generated by the differential expressions \[\N-y_j''(x_j) + q_j(x_j) y_j(x_j), \quad x_j \in e_j = (0, b_j), \quad j = 1, 2, \dots, m, \N\]\Nthe boundary conditions \N\[\Ny_j'(b_j) - h_j y_j(b_j) = 0, \quad j = 1, 2, \dots, m,\N\]\Nand the matching conditions: \N\[\Ny_1(0) = y_2(0) = \dots = y_m(0), \quad \sum_{j = 1}^m (y_j'(0) - k_j y_j(0)) = 0, \N\]\Nwhere \(q_j \in L_2(0, b_j)\), \(b_j\) and \(k_j\) are real constants. The authors show that a finite number of eigenvalues is sufficient for the unique recovery of the stiffness coefficients \(k_j\), \(j = 1, \dots, m\).