Polynomial averages converge to the product of integrals

被引：46

作者：

Frantzikinakis, N ^{[1
]}

Kra, B ^{[1
]}

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2005年 / 148卷 / 1期

基金：

美国国家科学基金会;

关键词：

Affine Transformation; Inverse Limit; Polynomial Sequence; Ergodic Average; Ergodic System;

D O I：

10.1007/BF02775439

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We answer a question posed by Vitaly Bergelson, showing that in a totally ergodic system, the average of a product of functions evaluated along polynomial times, with polynomials of pairwise differing degrees, converges in L-2 to the product of the integrals. Such averages are characterized by nilsystems and so we reduce the problem to one of uniform distribution of polynomial sequences on nilmanifolds.

引用

页码：267 / 276

页数：10

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