We study the separation from zero of a sequence ϕϕ to obtain the estimates of the form ϕ(n)/nϕ(n)/n for the rate of pointwise convergence of ergodic averages. Each of these ϕϕ is shown to be separated from zero for mixings which is not always so for weak mixings. Moreover, for the characteristic function of a nontrivial set, it is shown that there exists a measure preserving transformation with arbitrarily slow decay of ergodic averages.
Предметные области OECD FOS+WOS
- 1.01 МАТЕМАТИКА