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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 Nachbin's theorem ： ウィキペディア英語版 Nachbin's theorem In mathematics, in the area of complex analysis, Nachbin's theorem (named after Leopoldo Nachbin) is commonly used to establish a bound on the growth rates for an analytic function. This article will provide a brief review of growth rates, including the idea of a function of exponential type. Classification of growth rates based on type help provide a finer tool than big O or Landau notation, since a number of theorems about the analytic structure of the bounded function and its integral transforms can be stated. In particular, Nachbin's theorem may be used to give the domain of convergence of the generalized Borel transform, given below. ==Exponential type== (詳細はcomplex plane is said to be of exponential type if there exist constants ''M'' and τ such that :$|f(re^)|\backslash le\; Me^$ in the limit of $r\backslash to\backslash infty$. Here, the complex variable ''z'' was written as $z=re^$ to emphasize that the limit must hold in all directions θ. Letting τ stand for the infimum of all such τ, one then says that the function ''f'' is of ''exponential type τ''. For example, let $f(z)=\backslash sin(\backslash pi\; z)$. Then one says that $\backslash sin(\backslash pi\; z)$ is of exponential type π, since π is the smallest number that bounds the growth of $\backslash sin(\backslash pi\; z)$ along the imaginary axis. So, for this example, Carlson's theorem cannot apply, as it requires functions of exponential type less than π. 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「Nachbin's 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.