Sampling expansions associated with Kamke problems

Abstract.

The present paper is devoted to the derivation of sampling expansions for entire functions which are represented as integral transforms where a differential operator is acting on the kernels. The situation generalizes the results obtained in sampling theory associated with boundary value problems to the case when the differential equation has the form $N(y)=\lambda P(y),$ where N and P are two differential expressions of orders n and p respectively, $n>p$ and $\lambda$ is the eigenvalue parameter. Both self adjoint and non self adjoint cases will be considered with examples in which the boundary conditions are strongly regular.