Mathematics – Dynamical Systems
Scientific paper
2011-11-30
Mathematics
Dynamical Systems
v6: 26 p., including a generalizion of the "Roth theorem for amenable groups" due to Bergelson, McCutcheon and Zhang to averag
Scientific paper
Multiple ergodic averages corresponding to polynomial sequences in nilpotent
groups of measure preserving transformations converge in L^2, as was proved
recently by Walsh. We extend this result to averages along F{\o}lner nets in
amenable groups. We also generalize the "Roth theorem for amenable groups" due
to Bergelson, McCutcheon and Zhang to averages with arbitrarily many terms.
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