论文标题
超越亚伯群的线性重复性
Linear repetitivity beyond abelian groups
论文作者
论文摘要
我们表明，多项式生长的组中有线性重复的加权DeLone集具有独特的千古船体。该结果特别适用于使用符号替代方法在伴侣论文arxiv中构建的同质谎言组中线性重复的加权delone集。更普遍地，使用Ornstein-Weiss的准铺设方法，我们在新的重复条件下建立了在可能的单型LCSC基团中加权的Delone套件的独特性奇特性，我们称之为脾气暴躁。为此，我们建立了一个一般的亚添加融合定理，该定理还具有有关Banach密度的存在以及在Cayley图上有限跳跃范围运算符的光谱分布函数的均匀近似的应用。
We show that linearly repetitive weighted Delone sets in groups of polynomial growth have a uniquely ergodic hull. This result applies in particular to the linearly repetitive weighted Delone sets in homogeneous Lie groups constructed in the companion paper arXiv:2109.15210 using symbolic substitution methods. More generally, using the quasi-tiling method of Ornstein-Weiss, we establish unique ergodicity of hulls of weighted Delone sets in amenable unimodular lcsc groups under a new repetitivity condition which we call tempered repetitivity. For this purpose, we establish a general sub-additive convergence theorem, which also has applications concerning the existence of Banach densities and uniform approximation of the spectral distribution function of finite hopping range operators on Cayley graphs.
