IP-Dirichlet测度与IP-刚性动力系统：广义Riesz积方法
IP-Dirichlet measures and IP-rigid dynamical systems: an approach via generalized Riesz products
摘要：
如果$(n_{k})_{k\ge 1}$是严格递增的整数序列，单位圆$\mathbb{T}$上的连续概率测度$σ$称为关于$(n_{k})_{k\ge 1}$的IP-狄利克雷，如果作为$F$的$\hatσ(\sum_{k\in F}n_{k})\to 1 $遍历$\mathbb{N}$的所有非空有限子集$F$，并且$F$的最小值趋于无穷大. IP-Dirichlet测度及其与IP-刚性动力系统的联系最近由Aaronson，Hosseini和Lema-dichlet czyk研究。我们简化和推广他们的一些结果，使用的方法涉及广义Riesz产品。
英文摘要：
If $(n_{k})_{k\ge 1}$ is a strictly increasing sequence of integers, a continuous probability measure $σ$ on the unit circle $\mathbb{T}$ is said to be IP-Dirichlet with respect to $(n_{k})_{k\ge 1}$ if $\hatσ(\sum_{k\in F}n_{k})\to 1 $ as $F$ runs over all non-empty finite subsets $F$ of $\mathbb{N}$ and the minimum of $F$ tends to infinity. IP-Dirichlet measures and their connections with IP-rigid dynamical systems have been investigated recently by Aaronson, Hosseini and Lemańczyk. We simplify and generalize some of their results, using an approach involving generalized Riesz products.
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。
