Sampling integrodifferential transforms arising from second order differential operators

We give sampling theorems associated with boundary value problems whose dif ferential equations are of the form M(y) = lambda S(y), where M and S are d ifferential expressions of the second and first order respectively and the eigenvalue parameter may appear in the boundary conditions. The class of th e sampled functions is not a class of integral transforms as is the case in the classical sampling theory, but it is a class of integrodifferential tr ansforms. We use solutions of the problem as well as Green's function to de rive two sampling theorems.