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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク plurisubharmonic function ： ウィキペディア英語版 plurisubharmonic function In mathematics, plurisubharmonic functions (sometimes abbreviated as psh, plsh, or plush functions) form an important class of functions used in complex analysis. On a Kähler manifold, plurisubharmonic functions form a subset of the subharmonic functions. However, unlike subharmonic functions (which are defined on a Riemannian manifold) plurisubharmonic functions can be defined in full generality on complex analytic spaces. ==Formal definition== A function :$f\; \backslash colon\; G\; \backslash to\; ,$ with ''domain'' $G\; \backslash subset\; \}\; \backslash \}\backslash subset\; \}^n$ the function $z\; \backslash mapsto\; f(a\; +\; bz)$ is a subharmonic function on the set :$\backslash .$ In ''full generality'', the notion can be defined on an arbitrary complex manifold or even a Complex analytic space $X$ as follows. An upper semi-continuous function :$f\; \backslash colon\; X\; \backslash to$ is said to be plurisubharmonic if and only if for any holomorphic map $\backslash varphi\backslash colon\backslash Delta\backslash to\; X$ the function :$f\backslash circ\backslash varphi\; \backslash colon\; \backslash Delta\; \backslash to$ is subharmonic, where $\backslash Delta\backslash subset)$, called Levi matrix, with entries : $\backslash lambda\_=\backslash frac$ is positive semidefinite. Equivalently, a $C^2$-function ''f'' is plurisubharmonic if and only if $\backslash sqrt\backslash partial\backslash bar\backslash partial\; f$ is a positive (1,1)-form. 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「plurisubharmonic function」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.