Evolution equations of the truncated moments of the parton densities. A possible application

A possible application of the evolution equation for the truncated Mellin moments to determination of the parton distributions in the nucleon is presented. We find that the reconstruction of the initial parton densities at scale $Q_0^2$ from their truncated moments at a given scale $Q^2$ is exact and unique for small number of free parameters ($\le 3$), even for the limited $x$-region of experimental data. For larger number of adjustable parameters the obtained fits are not unique and one needs an additional knowledge of the small-$x$ behaviour of the parton densities to make the reconstruction procedure reliable. We apply successfully our method to HERMES and COMPASS spin-dependent valence quark data.