英语词汇“Domain of holomorphy”是什么意思，翻译、用法及简单造句-英汉双解词典-英汉网

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单词	Domain of holomorphy
释义	Domain of holomorphy 中文百科全纯域在数学的多复变函数论中，全纯域是在下述意义下为极大的区域：在其上存在一个全纯函数，使得不能延拓至更大的区域上。正式而言，在n维复空间 ${\mathbb{C}}^n$ 中的开集 $\Omega$ 称为全纯域，如果不存在非空开集 $U \subset \Omega$ 和 $V \subset {\mathbb{C}}^n$ ，其中 $V$ 是连通的， $V \not\subset \Omega$ ，以及 $U \subset \Omega \cap V$ ，使得对在 $\Omega$ 上的每个全纯函数 $f$ ，存在一个在 $V$ 上的全纯函数 $g$ ，在 $U$ 上有 $f = g$ 。当n = 1时，每个开集都是全纯域。但是，当n ≥ 2时，哈托格斯引理指出存在不是全纯域的区域。英语百科 Domain of holomorphy 全纯域 In mathematics, in the theory of functions of several complex variables, a domain of holomorphy is a set which is maximal in the sense that there exists a holomorphic function on this set which cannot be extended to a bigger set. Formally, an open set $\Omega$ in the n-dimensional complex space ${\mathbb{C}}^n$ is called a domain of holomorphy if there do not exist non-empty open sets $U \subset \Omega$ and $V \subset {\mathbb{C}}^n$ where $V$ is connected, $V \not\subset \Omega$ and $U \subset \Omega \cap V$ such that for every holomorphic function $f$ on $\Omega$ there exists a holomorphic function $g$ on $V$ with $f = g$ on $U$
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