Eigenvalues of periodic Sturm-Liouville problems by the Shannon-Whittaker sampling theorem

Abstract

We are concerned with the computation of eigenvalues of a periodic Sturm-Liouville problem using interpolation techniques in Paley-Wiener spaces. We shall approximate the Hill discriminant by sampling a few of its values and then find its zeroes which are the square roots of the eigenvalues. Computable error estimates are provided together with eigenvalue enclosures.