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

We are concerned with the computation of eigenvalues of a periodic Sturm-Li ouville problem using interpolation techniques in Paley-Wiener spaces. We s hall approximate the Hill discriminant by sampling a few of its Values and then find its zeroes which are the square roots of the eigenvalues. Computa ble error estimates are provided together with eigenvalue enclosures.