In this paper, we study the periodic Sturm-Liouville problem, defined on three non-intersecting intervals with four supplementary conditions which are imposed at two internal points of interaction, so-called
 transmission conditions. We first prove that eigenvalues real and system eigenfunctions is an orthogonal system. Secondly, some auxiliary initial-value problems transmittal-characteri...

In this paper we present a study on the analogous properties of discrete and continuous Sturm-Liouville problems arising in matrix analysis and differential equations, respectively. Green’s functions in both cases have analogous expressions in terms of the spectral data. Most of the results associated to inverse problems in both cases are identical. In particular, in both cases Weyl’s m-functio...