  In the present paper, an inverse result of approximation, i.e., a saturation
theorem for the sampling Kantorovich operators is derived, in the case of
uniform approximation for uniformly continuous and bounded functions on the
whole real line. In particular, here we prove that the best possible order of
approximation that can be achieved by the above sampling series is the order
one, otherwise the function being approximated turns to be a constant. The
above result is proved by exploiting a suitable representation formula which
relates the sampling Kantorovich series with the well-known generalized
sampling operators introduced by P.L. Butzer. At the end, some other
applications of such representation formula are presented, together with a
discussion concerning the kernels of the above operators for which such an
inverse result occurs.
