Pleasant extensions retaining algebraic structure, II

Tim Austin

Research output: Contribution to journalArticlepeer-review


In this paper, we combine the general tools developed in [5] with several ideas taken from earlier work on one-dimensional nonconventional ergodic averages by Furstenberg and Weiss [17], Host and Kra [21] and Ziegler [44] to study the averages (Formula presented.) associated to a triple of directions p1, p2, p3 ∈ ℤ2 that lie in general position along with 0 ∈ ℤ2. We show how to construct a “pleasant” extension of an initiallygiven ℤ2-system for which these averages admit characteristic factors with a very concrete description, involving the same structure as for those in [2] together with two-step pro-nilsystems (reminiscent of [21] and its predecessors). We also use this analysis to construct pleasant extensions and then prove norm convergence for the polynomial nonconventional ergodic averages (Formula presented.) associated to two commuting transformations T1, T2.

Original languageEnglish (US)
Pages (from-to)1-111
Number of pages111
JournalJournal d'Analyse Mathematique
Issue number1
StatePublished - Apr 20 2015

ASJC Scopus subject areas

  • Analysis
  • General Mathematics


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