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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 Stieltjes moment problem ： ウィキペディア英語版 Stieltjes moment problem In mathematics, the Stieltjes moment problem, named after Thomas Joannes Stieltjes, seeks necessary and sufficient conditions for a sequence to be of the form :$m\_n=\backslash int\_0^\backslash infty\; x^n\backslash ,d\backslash mu(x)\backslash ,$ for some measure ''μ''. If such a function ''μ'' exists, one asks whether it is unique. The essential difference between this and other well-known moment problems is that this is on a half-line [0, ∞), whereas in the Hausdorff moment problem one considers a bounded interval [0, 1], and in the Hamburger moment problem one considers the whole line (−∞, ∞). ==Existence== Let : m_1 & m_2 & m_3 & \cdots & m_ \\ m_2& m_3 & m_4 & \cdots & m_ \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ m_ & m_ & m_ & \cdots & m_ \end\right ) and : m_2 & m_3 & m_4 & \cdots & m_ \\ m_3 & m_4 & m_5 & \cdots & m_ \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ m_ & m_ & m_ & \cdots & m_ \end\right ). Then is a moment sequence of some measure on $[0,\backslash infty)$ with infinite support if and only if for all ''n'', both :$\backslash det(\backslash Delta\_n)\; >\; 0\backslash \; \backslash mathrm\backslash \; \backslash det\backslash left(\backslash Delta\_n^\backslash right)\; >\; 0.$ is a moment sequence of some measure on $[0,\backslash infty)$ with finite support of size ''m'' if and only if for all $n\; \backslash leq\; m$, both :$\backslash det(\backslash Delta\_n)\; >\; 0\backslash \; \backslash mathrm\backslash \; \backslash det\backslash left(\backslash Delta\_n^\backslash right)\; >\; 0$ and for all larger $n$ :$\backslash det(\backslash Delta\_n)\; =\; 0\backslash \; \backslash mathrm\backslash \; \backslash det\backslash left(\backslash Delta\_n^\backslash right)\; =\; 0.$ 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「Stieltjes moment problem」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.