Sampling for the fourth-order Sturm–Liouville differential operator

We extend the sampling method to compute the eigenvalues of a fourth-order differential operator. We show that the Shannon sampling theorem is not applicable due to the growth of the solutions on the real line. The inverse spectral theory, as developed by McLaughlin, and Kramer’s theorem allow us to express the characteristic function explicitly by a new sampling formula.  2003 Elsevier Science (USA). All rights reserved.