Aperiodic order and spherical diffraction, I: auto‐correlation of regular model sets
Aperiodic order and spherical diffraction, I: auto‐correlation of regular model sets
复制标题
非周期阶次和球面衍射，I：规则模型集的自相关
DOI：
10.1112/plms.12091
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发表时间：
2016
影响因子：
1.8
通讯作者：
Felix Pogorzelski
中科院分区：
文献类型：
--
作者：
M. Björklund;Tobias Hartnick;Felix Pogorzelski
我们研究了任意局部紧第二可数（lcsc）群中的一致和非一致模型集，这提供了Meyer定义的局部紧阿贝尔群中的一致模型集的自然推广，并用作准晶的数学模型。然后我们定义了任意lcsc群中有限局部复形子集的自相关概念，它将霍夫的经典定义推广到顺从群之外，并给出了正则模型集的自相关公式.沿着这条路，我们证明了任意正则模型集的穿孔船体允许唯一不变的概率测度，即使在穿孔船体是非紧的并且群是不顺从的情况下。事实上，这个测度也是相对于任何容许概率测度的唯一平稳测度。
We study uniform and non‐uniform model sets in arbitrary locally compact second countable (lcsc) groups, which provide a natural generalization of uniform model sets in locally compact abelian groups as defined by Meyer and used as mathematical models of quasi‐crystals. We then define a notion of auto‐correlation for subsets of finite local complexitiy in arbitrary lcsc groups, which generalizes Hof's classical definition beyond the class of amenable groups, and provide a formula for the auto‐correlation of a regular model set. Along the way we show that the punctured hull of an arbitrary regular model set admits a unique invariant probability measure, even in the case where the punctured hull is non‐compact and the group is non‐amenable. In fact this measure is also the unique stationary measure with respect to any admissible probability measure.
影响因子：
1.3
作者：
Gorodnik A
通讯作者：
Gorodnik A