The strong derivative of the best approximation operator

ABSTRACT

This article is devoted to the derivation of sampling series associated with eigenvalue problems. No examples of sampling theorems associated with odd order problems are known except when the order is one. Here we give necessary and sufficient conditions for the boundary conditions to be self adjoint. Then sampling series associated with odd order self adjoint and non self adjoint problems are given. The sampling representations associated with non self adjoint odd order problems are derived provided that the boundary condition are regular.