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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 Mercer's condition ： ウィキペディア英語版 Mercer's condition In mathematics, a real-valued function ''K(x,y)'' is said to fulfill Mercer's condition if for all square integrable functions ''g''(''x'') one has :$\backslash iint\; K(x,y)g(x)g(y)\backslash ,dx\; dy\; \backslash geq\; 0.$ This is analogous to the idea of a positive-semidefinite matrix, which is a matrix $M$ satisfying $z^Mz\backslash geq0$. The quantity $z^Mz$ can be thought of as a double sum, whereas the above integral is also analogous to a double sum. ==Examples== The constant function :$K(x,\; y)=1\backslash ,$ satisfies Mercer's condition, as then the integral becomes by Fubini's theorem :$\backslash iint\; g(x)g(y)\backslash ,dx\; dy\; =\; \backslash int\backslash !\; g(x)\; \backslash ,dx\; \backslash int\backslash !\; g(y)\; \backslash ,dy\; =\; \backslash left(\backslash int\backslash !\; g(x)\; \backslash ,dx\backslash right)^2$ which is indeed non-negative. 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「Mercer's condition」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.