  Successive differences on a sequence of data help to discover some smoothness
features of this data. This was one of the main reasons for rewriting the
classical interpolation formula in terms of such data differences. The aim of
this paper is to mimic them to a sequence of regular samples of a function in a
shift-invariant subspace allowing its stable recovery. A suitable expression
for the functions in the shift-invariant subspace by means of an isomorphism
with the $L^2(0,1)$ space is the key to identify the simple pattern followed by
the dual Riesz bases involved in the derived formulas. The paper contains
examples illustrating different non-exhaustive situations including also the
two-dimensional case.
