  Using the asymptotical minimax framework, we examine convergence rates
equivalency between a continuous functional deconvolution model and its
real-life discrete counterpart over a wide range of Besov balls and for the
$L^2$-risk. For this purpose, all possible models are divided into three
groups. For the models in the first group, which we call uniform, the
convergence rates in the discrete and the continuous models coincide no matter
what the sampling scheme is chosen, and hence the replacement of the discrete
model by its continuous counterpart is legitimate. For the models in the second
group, to which we refer as regular, one can point out the best sampling
strategy in the discrete model, but not every sampling scheme leads to the same
convergence rates; there are at least two sampling schemes which deliver
different convergence rates in the discrete model (i.e., at least one of the
discrete models leads to convergence rates that are different from the
convergence rates in the continuous model). The third group consists of models
for which, in general, it is impossible to devise the best sampling strategy;
we call these models irregular. We formulate the conditions when each of these
situations takes place. In the regular case, we not only point out the number
and the selection of sampling points which deliver the fastest convergence
rates in the discrete model but also investigate when, in the case of an
arbitrary sampling scheme, the convergence rates in the continuous model
coincide or do not coincide with the convergence rates in the discrete model.
We also study what happens if one chooses a uniform, or a more general
pseudo-uniform, sampling scheme which can be viewed as an intuitive replacement
of the continuous model.
