  The classical Kramer sampling theorem establishes general conditions that
allow the reconstruction of functions by mean of orthogonal sampling formulae.
One major task in sampling theory is to find concrete, non trivial realizations
of this theorem. In this paper we provide a new approach to this subject on the
basis of the M. G. Krein's theory of representation of simple regular symmetric
operators having deficiency indices (1,1). We show that the resulting sampling
formulae have the form of Lagrange interpolation series. We also characterize
the space of functions reconstructible by our sampling formulae. Our
construction allows a rigorous treatment of certain ideas proposed recently in
quantum gravity.
