Inverse problems for the Sturm-Liouville operator with discontinuity conditions (Q2334936)

The authors continue their study of a boundary value problem generated by the one-dimensional Schrödinger equation on a finite interval together with the Dirichlet boundary conditions and a discontinuity condition at an interior point of the interval, begun in [\textit{H. M. Huseynov} and \textit{F. Z. Dostuyev}, Trans. Natl. Acad. Sci. Azerb., Ser. Phys.-Tech. Math. Sci. 34, No. 1, Math. Mech., 57--66 (2014; Zbl 1333.34126)]. In this paper, they obtain some necessary and sufficient conditions for two sequences of real numbers to be the eigenvalues and the norming constants of this boundary value problem (respectively, to be the spectra of this problem and a similar problem with the Dirichlet conditions replaced by the Dirichlet-Neumann conditions).