论文标题
用于通勤转换和应用多项式序列的关节终止性
Joint ergodicity for commuting transformations and applications to polynomial sequences
论文作者
论文摘要
我们提供了相关的序列收集序列汇总系统的必要条件。将这些结果与一种新技术相结合，我们称之为“半摩托平滑”，我们解决了与多项式迭代通勤转换的多个Ergodic平均值相关的几个猜想。我们表明，宿主-KRA因子是成对独立多项式的特征，并且在某些登山性条件下，相关的ergodic平均值收敛于积分的产物。此外，当多项式是线性独立的时，我们表明有理的kronecker因子是特征性的，并且针对相关的多重复发问题推断了khintchine型的下限。最后，我们证明了一个nil加无效的分解结果，用于在由成对独立多项式的家族给出迭代的情况下通勤转换的多个相关序列。
We give necessary and sufficient conditions for joint ergodicity results of collections of sequences with respect to systems of commuting measure preserving transformations. Combining these results with a new technique that we call "seminorm smoothening", we settle several conjectures related to multiple ergodic averages of commuting transformations with polynomial iterates. We show that the Host-Kra factor is characteristic for pairwise independent polynomials, and that under certain ergodicity conditions the associated ergodic averages converge to the product of integrals. Moreover, when the polynomials are linearly independent, we show that the rational Kronecker factor is characteristic and deduce Khintchine-type lower bounds for the related multiple recurrence problem. Finally, we prove a nil plus null decomposition result for multiple correlation sequences of commuting transformations in the case where the iterates are given by families of pairwise independent polynomials.
