TY - JOUR
T1 - Convergence of multiple ergodic averages for some commuting transformations
AU - Frantzikinakis, Nikos
AU - Kra, Bryna
PY - 2005/6
Y1 - 2005/6
N2 - We prove the L2-convergence for the linear multiple ergodic averages of commuting transformations T1,..., T2), assuming that each map 7i and each pair 7iT j-1 is ergodic for i ≠ j. The limiting behavior of such averages is controlled by a particular factor, which is an inverse limit of nilsystems. As a corollary we show that the limiting behavior of linear multiple ergodic averages is the same for commuting transformations.
AB - We prove the L2-convergence for the linear multiple ergodic averages of commuting transformations T1,..., T2), assuming that each map 7i and each pair 7iT j-1 is ergodic for i ≠ j. The limiting behavior of such averages is controlled by a particular factor, which is an inverse limit of nilsystems. As a corollary we show that the limiting behavior of linear multiple ergodic averages is the same for commuting transformations.
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U2 - 10.1017/S0143385704000616
DO - 10.1017/S0143385704000616
M3 - Article
AN - SCOPUS:19844367012
VL - 25
SP - 799
EP - 809
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
SN - 0143-3857
IS - 3
ER -