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    ASSANI, IDRIS and MOORE, RYO 2015. A good universal weight for nonconventional ergodic averages in norm. Ergodic Theory and Dynamical Systems, p. 1.

    Eisner, Tanja 2013. Linear Sequences and Weighted Ergodic Theorems. Abstract and Applied Analysis, Vol. 2013, p. 1.

  • Ergodic Theory and Dynamical Systems, Volume 34, Issue 5
  • October 2014, pp. 1747-1760

Cube spaces and the multiple term return times theorem

  • DOI:
  • Published online: 14 March 2013

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.

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I. Assani , E. Lesigne and D. Rudolph . Wiener–Wintner return-times ergodic theorem. Israel J. Math. 92 (1–3) (1995), 375395.

J. Bourgain , H. Furstenberg , Y. Katznelson and D. S. Ornstein . Appendix on return-time sequences. Publ. Math. Inst. Hautes Études Sci. 69 (1989), 4245.

G. D. Birkhoff . Proof of the ergodic theorem. Proc. Natl Acad. Sci. USA 17 (1931), 656660.

B. Host and B. Kra . Nonconventional ergodic averages and nilmanifolds. Ann. of Math. (2) 161 (1) (2005), 397488.

B. Host and B. Kra . Uniformity seminorms on ${\ell }^{\infty } $ and applications. J. Anal. Math. 108 (2009), 219276.

B. Host , B. Kra and A. Maass . Nilsequences and a structure theorem for topological dynamical systems. Adv. Math. 224 (1) (2010), 103129.

A. Leibman . Pointwise convergence of ergodic averages for polynomial sequences of translations on a nilmanifold. Ergod. Th. & Dynam. Sys. 25 (1) (2005), 201213.

E. Lindenstrauss . Pointwise theorems for amenable groups. Invent. Math. 146 (2) (2001), 259295.

D. Ornstein and B. Weiss . Subsequence ergodic theorems for amenable groups. Israel J. Math. 79 (1) (1992), 113127.

D. J. Rudolph . Eigenfunctions of $T\times S$ and the Conze–Lesigne algebra. Ergodic Theory and its Connections with Harmonic Analysis (Alexandria, 1993) (London Mathematical Society Lecture Note Series, 205). Cambridge University Press, Cambridge, 1995, pp. 369432.

D. J. Rudolph . Fully generic sequences and a multiple-term return-times theorem. Invent. Math. 131 (1) (1998), 199228.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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