论文标题
在$ {\ mathbb c}^n $中定义的全体形态功能的范围保留恒定功能的扩展
Norm Preserving Extensions of Holomorphic Functions Defined on Varieties in ${\mathbb C}^n$
论文作者
论文摘要
如果$ v $是pseudoconvex域$ω$中的一个分析设置，我们表明，总有一个包含$ v $的pseudoconvex域$ g \subseteqΩ$，并且具有每个有界的holomorphic函数的属性，即$ v $在$ g $上扩展到$ g $的$ V $。我们为某些特定的分析集找到了这样的$ G $。 当$ω$是一个操作系统时，我们表明$ v $上的全态函数有一个规范，可以通过扩展到$ω$保存，并且可以保留。
If $V$ is an analytic set in a pseudoconvex domain $Ω$, we show there is always a pseudoconvex domain $G \subseteq Ω$ that contains $V$ and has the property that every bounded holomorphic function on $V$ extends to a bounded holomorphic function on $G$ with the same norm. We find such a $G$ for some particular analytic sets. When $Ω$ is an operhedron we show there is a norm on holomorphic functions on $V$ that can always be preserved by extensions to $Ω$.
