翻訳と辞書 Words near each other ・ Pseudocomotis albolineana ・ Pseudocomotis chingualana ・ Pseudocomotis citroleuca ・ Pseudocomotis nortena ・ Pseudocomotis razowskii ・ Pseudocomotis scardiana ・ Pseudocomotis serendipita ・ Pseudocompact space ・ Pseudocomplement ・ Pseudoconalia ・ Pseudoconizonia basalis ・ Pseudoconorbis ・ Pseudoconsensus ・ Pseudoconversational transaction ・ Pseudoconvex function ・ Pseudoconvexity ・ Pseudocopaeodes ・ Pseudocopaeodes eunus ・ Pseudocopicucullia ・ Pseudocopivaleria ・ Pseudocoptops seychellarum ・ Pseudocopulation ・ Pseudocoraebus ・ Pseudocordylus ・ Pseudocoremia ・ Pseudocoremia fenerata ・ Pseudocoremia leucelaea ・ Pseudocoremia melinata ・ Pseudocoremia suavis ・ Pseudocoris Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Pseudoconvexity ： ウィキペディア英語版 Pseudoconvexity In mathematics, more precisely in the theory of functions of several complex variables, a pseudoconvex set is a special type of open set in the ''n''-dimensional complex space C''n''. Pseudoconvex sets are important, as they allow for classification of domains of holomorphy. Let :$G\backslash subset$ is a relatively compact subset of $G$ for all real numbers $x.$ In other words, a domain is pseudoconvex if $G$ has a continuous plurisubharmonic exhaustion function. Every (geometrically) convex set is pseudoconvex. When $G$ has a $C^2$ (twice continuously differentiable) boundary, this notion is the same as Levi pseudoconvexity, which is easier to work with. More specifically, with a $C^2$ boundary, it can be shown that $G$ has a defining function; i.e., that there exists $\backslash rho:\; \backslash mathbb^n\; \backslash to\; \backslash mathbb$ which is $C^2$ so that $G=\backslash$, and $\backslash partial\; G\; =\backslash$. Now, $G$ is pseudoconvex iff for every $p\; \backslash in\; \backslash partial\; G$ and $w$ in the complex tangent space at p, that is, :$\backslash nabla\; \backslash rho(p)\; w\; =\; \backslash sum\_^n\; \backslash fracw\_j\; =0$, we have :$\backslash sum\_^n\; \backslash frac\; w\_i\; \backslash bar\; \backslash geq\; 0.$ If $G$ does not have a $C^2$ boundary, the following approximation result can come in useful. Proposition 1 ''If $G$ is pseudoconvex, then there exist bounded, strongly Levi pseudoconvex domains $G\_k\; \backslash subset\; G$ with $C^\backslash infty$ (smooth) boundary which are relatively compact in $G$, such that'' :$G\; =\; \backslash bigcup\_^\backslash infty\; G\_k.$ This is because once we have a $\backslash varphi$ as in the definition we can actually find a ''C''∞ exhaustion function. ==The case ''n'' = 1== In one complex dimension, every open domain is pseudoconvex. The concept of pseudoconvexity is thus more useful in dimensions higher than 1. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Pseudoconvexity」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.