The regular sampling problem is usually related to classical work of
Shannon, who has shown that band-limited functions in $L^2(R)$ can be
reconstructed from their regular samples, if the Nyquist criterion
is satisfied. There are many variations to this theme, taking other
function spaces into account, which allow to grasp better the
locality of the reconstruction, or even reconstruct from irregular
samples, using iterative methods. For me {\it Wiener amalgam spaces}
are the natural setting, because they provide methods to control
the convergence in different function spaces or control jitter errors.

The early work on sampling by Paul Butzer clearly shows the close
connection to Poisson's formula. It results in the statement that
the Dirac comb (viewed as a mild distribution) has the Dirac comb
of the dual lattice as its Fourier transform. Thus sampling on the
time side corresponds to periodization on the frequency side.
For this way of looking at sampling we may use the Banach Gelfand
triple $(SO,L2,SO^*)$, which arose in time-frequency analysis.

The talk will discuss a few topics closely connected to the question
whether a function in $SO(R)$ can be approximately reconstructed
from regular samples, if they are taken over a sufficiently fine
grid and over a sufficiently large interval. The approach takes
a combined periodization sampling operator as the starting point
and starts the analysis by looking at its spreading representation.
Obviously it can be viewed as a mapping from $SO(R)$ into $C^N$
\newline (for sufficiently large $N$), or equivalently as a bounded linear mapping from $SO(R)$ into $SO^*(R)$.
A corresponding paper is under preparation.