  The influence of the finite sizes on the coherent properties of 3D Bose
systems is considered. As is shown, the correlation functions of a Bose gas in
a trap have essential differences from analogous correlation functions in an
infinite system. Thus, the anomalous correlation function vanishes due to the
divergency of phase fluctuations which destruct the order parameter too. The
normal correlation function decays exponentially in time for sufficiently large
time interval.
