Pointwise characteristic factors for the multiterm return times theorem

DOI10.1017/S0143385711000769zbMath1266.37004arXiv1012.3132MaRDI QIDQ2908137

Idris Assani, Kimberly J. Presser

Publication date: 4 September 2012

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.3132

zbMATH Keywords

Szemerédi theoremvan der Corput lemmareturn times theoremcharacteristic factorHost-Kra-Ziegler factorKronecker factor\(k\)-step distal factornon-conventionnel averages

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30)

Related Items (6)

Some open problems on multiple ergodic averages ⋮ Cube spaces and the multiple term return times theorem ⋮ Linear sequences and weighted ergodic theorems ⋮ A good universal weight for nonconventional ergodic averages in norm ⋮ Pointwise characteristic factors for Wiener–Wintner double recurrence theorem ⋮ Generic properties of extensions

Cites Work

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• Pointwise ergodic theorems for arithmetic sets. With an appendix on return-time sequences, jointly with Harry Furstenberg, Yitzhak Katznelson and Donald S. Ornstein
• Pointwise convergence of ergodic averages along cubes
• Ergodic behavior of diagonal measures and a theorem of Szemeredi on arithmetic progressions
• Fully generic sequences and a multiple-term return-times theorem
• Wiener-Wintner return-times ergodic theorem
• Multiple return times theorems for weakly mixing systems
• Nonconventional ergodic averages and nilmanifolds
• Universal characteristic factors and Furstenberg averages
• A joinings proof of Bourgain's return time theorem
• Proof of the Ergodic Theorem
• The Structure of Distal Flows

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