论文标题
泰勒的通用泰勒系列在几个变量中取决于参数
Universal Taylor Series in several variables depending on parameters
论文作者
论文摘要
我们在产品上建立了通用泰勒系列的通用生存，$ω= \ prodω_i$ of Planar简单连接域$ω_i$，其中通用近似在产品$ k $的平面紧凑型套件上，带有连接的补充，提供$ k \capΩ= \ emptyset $。这些类是关于一个或几个扩展中心的，通用近似位于函数级别或所有衍生物的水平。另外，只要$ k \ cap \overlineΩ= \ emptySet $和$ \ {\ infty \} \ cup [\ mathbb {c} \ setMinus \overlineΩ_i] $已连接到所有$ i $。以前的所有类型的通用系列都可能取决于某些参数。然后，近似功能可能取决于相同的参数，如本文所示。这些普遍性在拓扑和代数上是通用的。
We establish generic existence of Universal Taylor Series on products $Ω= \prod Ω_i$ of planar simply connected domains $Ω_i$ where the universal approximation holds on products $K$ of planar compact sets with connected complements provided $K \cap Ω= \emptyset$. These classes are with respect to one or several centers of expansion and the universal approximation is at the level of functions or at the level of all derivatives. Also, the universal functions can be smooth up to the boundary, provided that $K \cap \overlineΩ = \emptyset$ and $\{\infty\} \cup [\mathbb{C} \setminus \overlineΩ_i]$ is connected for all $i$. All previous kinds of universal series may depend on some parameters; then the approximable functions may depend on the same parameters, as it is shown in the present paper. These universalities are topologically and algebraically generic.
