ABSTRACT
In Chapter 4 we discussed sampling theorems associated with regular and singular Sturm-Liouville boundary-value problems and showed that if a Weiss-Kramer-type sampling theorem exists for such problems, then the associated sampling series is a Lagrange-type interpolation series. We also know that although almost all the known examples associated with Kramer’s theorem arise from Sturm-Liouville problems, the theorem is true for any regular self-adjoint boundary-value problem whose eigenfunctions are all generated by one single function, when the eigenvalue parameter λ is replaced by the eigenvalues.
