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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 Carathéodory kernel theorem ： ウィキペディア英語版 Carathéodory kernel theorem In mathematics, the Carathéodory kernel theorem is a result in complex analysis and geometric function theory established by the Greek mathematician Constantin Carathéodory in 1912. The uniform convergence on compact sets of a sequence of holomorphic univalent functions, defined on the unit disk in the complex plane and fixing 0, can be formulated purely geometrically in terms of the limiting behaviour of the images of the functions. The kernel theorem has wide application in the theory of univalent functions and in particular provides the geometric basis for the Loewner differential equation. ==Kernel of a sequence of open sets== Let ''U''''n'' be a sequence of open sets in C containing 0. Let ''V''''n'' be the connected component of the interior of ''U''''n'' ∩ ''U''''n'' + 1 ∩ ... containing 0. The kernel of the sequence is defined to be the union of the ''V''''n'''s, provided it is non-empty; otherwise it is defined to be $\backslash$. Thus the kernel is either a connected open set containing 0 or the one point set $\backslash$. The sequence is said to converge to a kernel if each subsequence has the same kernel. Examples *If ''U''''n'' is an increasing sequence of connected open sets containing 0, then the kernel is just the union. *If ''U''''n'' is a decreasing sequence of connected open sets containing 0, then, if 0 is an interior point of ''U''1 ∩ ''U''2 ∩ ..., the sequence converges to the component of the interior containing 0. Otherwise, if 0 is not an interior point, the sequence converges to $\backslash$. 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「Carathéodory kernel theorem」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.