论文标题
混合序列非混合转换和组动作
Mixing sequences for non-mixing transformations and group actions
论文作者
论文摘要
我们确定有一些非混合图在适当的序列上混合在一起，包括序列$（s_i）$，可以满足Rajchman分离的属性。我们的示例基于楼梯排名一号建筑，$ m $ the的构造和高斯转型。结果，我们获得了沿正方形混合的非混合图。我们进一步证明了序列$ m =（m_n）$是某些弱混合$ {1}/{2} $的混合序列，而刚性转换$ t $ i时，并且仅当$ m $的补充是厚的集合。该结果被推广到$ {r}/{（R+1）} $ - $ r \ in \ mathbb {n} $的刚性变换。此外，通过将谐波分析的连续性集对宿主parreau表征，我们将结果扩展到了无限的可计数阿贝尔小组动作。
We establish that there are non-mixing maps that are mixing on appropriate sequences including sequences $(s_i)$ which satisfy the Rajchman dissociated property. Our examples are based on the staircase rank one construction, $M$-towers constructions and the Gaussian transformations. As a consequence, we obtain there are non-mixing maps which are mixing along the squares. We further prove that a sequence $M=(m_n)$ is a mixing sequence for some weak mixing ${1}/{2}$-rigid transformation $T$ if and only if the complement of $M$ is a thick set. This result is generalized to ${r}/{(r+1)}$-rigid transformations for $r\in \mathbb{N}$. Moreover, by applying Host-Parreau characterization of the set of continuity from Harmonic Analysis, we extend our results to the infinite countable abelian group actions.
