Comments on eigenfunction expansions of discontinuous Sturm-Liouville systems

In earlier works [4],[5] we examined the eigenfunctions of Sturm-Liouville systems of the form -y″(x) + q(x)y(x) = λy(x) on a bounded interval having eigenfunctions with jump discontinuities. An eigenfunction expansion theorem for these discontinuous Sturm-Liouville problems along with applications of the theory were presented. In this note we review earlier results and examine the possibilities for extending our results to general, single and multiple discontinuity cases. © 1989.