Error Estimation for Reconstruction of a Signal from a Finite Sample

We present an exact error estimate for the reconstruction of signals of the form
$$ f(z)=\int_{G}g(z,t)u(t)\,dt $$
from samples $\omega_k=f(z_k)$, $k=1,\dots,n$, for reconstruction according to the generalized sampling theorem. Ways for reducing the error are shown.