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Pointwise ergodic theorems for higher levels of mixing

Volume 261 / 2021

Sohail Farhangi Studia Mathematica 261 (2021), 329-344 MSC: Primary 37A25, 37A30; Secondary 37A05, 28D05. DOI: 10.4064/sm200915-22-5 Published online: 9 August 2021

Abstract

We prove strengthenings of the Birkhoff Pointwise Ergodic Theorem for weakly mixing and strongly mixing measure preserving systems. We show that our pointwise theorem for weakly mixing systems is strictly stronger than the Wiener–Wintner Theorem. We also show that our pointwise theorems for weakly mixing and strongly mixing systems characterize those systems.

Authors

  • Sohail FarhangiDepartment of Mathematics
    The Ohio State University
    Mathematics Building 430
    Columbus, OH 43220, U.S.A.
    e-mail

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