Correlations and rates of convergence in general ergodic theorems

In the ergodic theorem for unitary actions of Hausdorff locally compact second-countable groups, a formula is obtained for calculation of the norms of deviations of ergodic averages from their limit using known correlations. Illustrative examples are given. We also examine the inverse problem for recovery of sums of some sets of correlations from the known values of the norms of these deviations.