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 ω(x), we will show that the spectral sets {λn(q, ha, hk)}k=1+∞ and {λ−n(q, hb, hk)}k=1+∞ for distinct hk are sufficient to determine the potential q(x) on the finite interval [a, b] and coefficients ha and hb of the boundary conditions.