  In this paper, we investigate the sampling analysis for a new Sturm-Liouville
problem with symmetrically located discontinuities which are defined to
depending on 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 needed
relations for the derivations of the sampling theorems and construct Green's
function for the problem. Then we derive sampling representations for
transforms whose kernels are either solutions or Green's functions.
