论文标题
Seleznev的通用功率系列，带有几个变量的参数
Universal power series of Seleznev with parameters in several variables
论文作者
论文摘要
我们将Seleznev的通用功率系列推广到几个变量，并允许系数取决于参数。然后，近似功能可能取决于相同的参数。通用近似值$ k = \ displayStyle \ prod_ {i = 1}^d k_i $，其中$ k_i \ subseteq \ mathbb {c} $是紧凑的集合和$ \ mathbb {c} \ setminus k_i $ n.在这样的$ k $上，部分总和均匀地概述了任何多项式。最后，部分总和可以被更一般的表达式取代。这种现象在拓扑和代数上是通用的。
We generalize the universal power series of Seleznev to several variables and we allow the coefficients to depend on parameters. Then, the approximable functions may depend on the same parameters. The universal approximation holds on products $K = \displaystyle\prod_{i = 1}^d K_i$, where $K_i \subseteq \mathbb{C}$ are compact sets and $\mathbb{C} \setminus K_i$ are connected, $i = 1, \dots, d$ and $0 \notin K$. On such $K$ the partial sums approximate uniformly any polynomial. Finally, the partial sums may be replaced by more general expressions. The phenomenon is topologically and algebraically generic.
