Random Sequences and Pointwise Convergence of Multiple Ergodic Averages

被引：18

作者：

Frantzikinakis, N. ^{[1
]}

Lesigne, E. ^{[2
]}

Wierdl, M. ^{[3
]}

机构：

[1] Univ Crete, Dept Math, Iraklion 71409, Greece

[2] Univ Tours, Federat Rech Denis Poisson, Lab Math & Phys Theor, UMR CNRS 6083, F-37200 Tours, France

[3] Univ Memphis, Dept Math, Memphis, TN 38152 USA

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2012年 / 61卷 / 02期

基金：

美国国家科学基金会;

关键词：

ergodic averages; mean convergence; pointwise convergence; multiple recurrence; random sequences; commuting transformations; COMMUTING TRANSFORMATIONS; DIAGONAL MEASURES; THEOREMS; RECURRENCE; INTEGERS; SYSTEMS; GROWTH;

D O I：

10.1512/iumj.2012.61.4571

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove pointwise convergence, as N -> infinity, for the multiple ergodic averages (1/N) Sigma(N)(n=1) f(T(n)x) . g(S(an)x), where T and S are commuting measure preserving transformations, and a(n) is a random version of the sequence [n(c)] for some appropriate c > 1. We also prove similar mean convergence results for averages of the form (1/N) Sigma(N)(n=1) f(T(an)x) . g(S(an)x), as well as pointwise results when T and S are powers of the same transformations. The deterministic versions of these results, where one replaces a(n) with [n(c)], remain open, and we hope that our method will indicate a fruitful way to approach these problems as well.

引用

页码：585 / 617

页数：33