In this paper we consider the eigenfunction expansions associated with Fredholm integral equations of first kind when the data are perturbed by noise. We prove that these expansions are asymptotically convergent, in the sense of L2-norm, when the bound of

This paper is concerned with the existence of piecewise analytic optimal solutions for various linear optimal control problems with piecewise analytic problem data. Some results of this form may be found in the literature but their proofs are generally based on the maximum principle and require certain normality conditions before they can be applied. Also the control constraints are required to be polyhedral and fixed in time. Using the recent theory developed for a class of problems known as separated continuous linear programs we are able to remove the normality conditions completely and allow time varying control constraints of both polyhedral and integral form. In particular, we prove theorems on the existence of piecewise analytic optimal solutions for the linear time-optimal control problem and the linear optimal control problem with or without end point constraints. Q 1996 Academic Press, Inc.