A uniqueness theorem for indefinite Sturm-Liouville operators

In this paper, we discuss the inverse problem for indefinite Sturm-Liouville operators on the finite interval [a, b]. For a fixed index n(n = 0, 1, 2, ??), given the weight function ??(x), we will show that the spectral sets {?? _n (q, h _a , h _k )} _k=1 ^+?? and {?? _?n (q, h _b , h _k )} _k=1 ^+?? for distinct h _k are sufficient to determine the potential q(x) on the finite interval [a, b] and coefficients h _a and h _b of the boundary conditions.