On the uniqueness of inverse spectral problems associated with incomplete spectral data

The inverse spectral problem for a Sturm-Liouville problem which consists of a Sturm-Liouville equation defined on the interval [0,a] and two separated boundary conditions at the endpoints 0 and a, one of which is involved function f(λ), is considered in this paper. When f(λ) is the type of Herglotz functions and is known as a priori, we prove that the potential on [0,a] and the other boundary condition can be uniquely determined in terms of appropriate partial information on the spectrum and partial information on the set of normalizing constants.