ON LAGRANGE INTERPOLATION AND KRAMER-TYPE SAMPLING THEOREMS ASSOCIATED WITH STURM-LIOUVILLE PROBLEMS

This article is devoted to a connection between Kramer's sampling theorem and sampling expansions generated by Lagrange interpolation. It is shown that any function that has a sampling expansion in the scope of Kramer's theorem also has a Lagrange-type interpolation expansion provided that the kernel associated with Kramer's theorem arises from a second-order Sturm-Liouville boundary-value problem. This new approach, which for a variety of regular and singular Sturm-Liouville problems leads to associated sampling theorems, recovers not only many known sampling expansions but also gives new ways to calculate the corresponding sampling functions. New sampling series are included.