Ergodic averages with generalized weights
Volume 173 / 2006
Studia Mathematica 173 (2006), 103-128
MSC: Primary 28D05; Secondary 37A99.
DOI: 10.4064/sm173-2-1
Abstract
Two types of weighted ergodic averages are studied. It is shown that if $F=\{ F_n\} $ is an admissible superadditive process relative to a measure preserving transformation, then a Wiener–Wintner type result holds for $F$. Using this result new good classes of weights generated by such processes are obtained. We also introduce another class of weights via the group of unitary functions, and study the convergence of the corresponding weighted averages. The limits of such weighted averages are also identified.
