多项式逼近收敛于积分乘积
Polynomial Averages Converge to the Product of Integrals
摘要：
我们回答了一个问题所提出的维塔利Bergelson，表明在一个完全遍历系统，平均产品的功能评估沿多项式倍，多项式的成对不同程度，收敛于$L^{2}$的产品的积分。这样的平均值的特点是由nilsystems，所以我们减少了问题的均匀分布的多项式序列的nilmanifold。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
