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 (lambda), is considered in this paper. When f (lambda) 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. (C) 2018 Elsevier Inc. All rights reserved.