On the equivalence of Kramer's and Shannon's sampling theorems (Corresp.)

The question of Campbell concerning the possibility of applying Shannon's sampling theorem to the same functions that can be sampled by Kramer's generalized sampling theorem is investigated and illustrated for more functions which are solutions of second-order differential equations with singular coefficients. A few definitions are introduced and some theorems are proved to show, in a more precise way, that under certain conditions the two sampling theorems are equivalent.