This paper is concerned with the generation of Kramer analytic kernels from first-order, linear, ordinary boundary-value problems. These kernels are obtained from boundary-value problems that are represented by self-adjoint differential operators. Necessary and sufficient conditions are given to ensure that these differential operators have a discrete spectrum which then allows of the introduction of the associated Kramer analytic kernel. An example is considered which leads to the important Shannon-Whittaker interpolation expansion theorem. (C) 2002 Elsevier Science B.V. All rights reserved.