  In this paper, we extend the correspondence between Bayesian estimation and
optimal smoothing in a Reproducing Kernel Hilbert Space (RKHS) adding a convexe
constraints on the solution. Through a sequence of approximating Hilbertian
spaces and a discretized model, we prove that the Maximum A Posteriori (MAP) of
the posterior distribution is exactly the optimal constrained smoothing
function in the RKHS. This paper can be read as a generalization of the paper
[7] of Kimeldorf-Wahba where it is proved that the optimal smoothing solution
is the mean of the posterior distribution.
