Cube spaces and the multiple term return times theorem

Abstract

We give a new proof of Rudolph's multiple term return times theorem based on Host-Kra structure theory. Our approach provides characteristic factors for all terms, works for arbitrary tempered Følner sequences and also yields a multiple term Wiener-Wintner-type return times theorem for nilsequences.

v2: 13 p., main result has been extended to tempered Følner sequences

References in corpus (2)

• Uniformity in the Wiener-Wintner theorem for nilsequences
• Return times theorem for amenable groups

Cited by in corpus (1)

• A good universal weight for nonconventional ergodic averages in norm