Sampling theorems for Sturm-Liouville problem with moving discontinuity points

Abstract

In this paper, we investigate the sampling analysis for a new Sturm-Liouville problem with symmetrically located discontinuities which are defined depending on a parameter in a neighborhood of a midpoint of the interval. Also the problem has transmission conditions at these points of discontinuity and includes an eigenparameter in a boundary condition. We establish briefly the relations needed for the derivations of the sampling theorems and construct the Green’s function for the problem. Then we derive sampling representations for the solutions and Green’s functions.