半拓扑半群上的一类远端函数
A Class of Distal Functions on Semitopological Semigroups
摘要：
在\cite{S}中研究了由$({\mathbb {Z}}, +)$上的函数的集合$\{n\mapsto λ^{n^k}:$ $λ\in{\mathbb {T}}$和$k\in{\mathbb{N}}\}$生成的代数的范数闭包（称为Weyl代数）.本文利用Namioka的一个结果，将该代数推广到一般的拓扑半群上，并证明了所涉及的代数的元素是distal的.特别是，我们研究这个代数的$({\mathbb {Z}}, +)$和（更一般地）的离散（添加剂）组的任何可数环。最后，我们的结果被处理的双循环半群。
英文摘要：
The norm closure of the algebra generated by the set $\{n\mapsto λ^{n^k}:$ $λ\in{\mathbb {T}}$ and $k\in{\mathbb{N}}\}$ of functions on $({\mathbb {Z}}, +)$ was studied in \cite{S} (and was named as the Weyl algebra). In this paper, by a fruitful result of Namioka, this algebra is generalized for a general semitopological semigroup and, among other things, it is shown that the elements of the involved algebra are distal. In particular, we examine this algebra for $({\mathbb {Z}}, +)$ and (more generally) for the discrete (additive) group of any countable ring. Finally, our results are treated for a bicyclic semigroup.
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。
