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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 Monodromy theorem ： ウィキペディア英語版 Monodromy theorem In complex analysis, the monodromy theorem is an important result about analytic continuation of a complex-analytic function to a larger set. The idea is that one can extend a complex-analytic function (from here on called simply ''analytic function'') along curves starting in the original domain of the function and ending in the larger set. A potential problem of this analytic continuation along a curve strategy is there are usually many curves which end up at the same point in the larger set. The monodromy theorem gives sufficient conditions for analytic continuation to give the same value at a given point regardless of the curve used to get there, so that the resulting extended analytic function is well-defined and single-valued. Before stating this theorem it is necessary to define analytic continuation along a curve and study its properties. ==Analytic continuation along a curve== The definition of analytic continuation along a curve is a bit technical, but the basic idea is that one starts with an analytic function defined around a point, and one extends that function along a curve via analytic functions defined on small overlapping disks covering that curve. Formally, consider a curve (a continuous function) $\backslash gamma:(1)\backslash to\; \backslash mathbb\; C.$ Let $f$ be an analytic function defined on an open disk $U$ centered at $\backslash gamma(0).$ An ''analytic continuation'' of the pair $(f,\; U)$ along $\backslash gamma$ is a collection of pairs $(f\_t,\; U\_t)$ for $0\backslash le\; t\backslash le\; 1$ such that * $f\_0=f$ and $U\_0=U$ * For each $t\backslash in\; (1),$ $U\_t$ is an open disk centered at $\backslash gamma(t)$ and $f\_t:U\_t\backslash to\backslash mathbb\; C$ is an analytic function * For each $t\backslash in\; (1)$ there exists $\backslash varepsilon\; >0$ such that for all $t\text{'}\backslash in\; (1)$ with one has that $\backslash gamma(t\text{'})\backslash in\; U\_t$ (which implies that $U\_t$ and $U\_$ have a non-empty intersection) and the functions $f\_t$ and $f\_$ coincide on the intersection $U\_t\backslash cap\; U\_.$ 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「Monodromy 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.