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Landau–Kolmogorov inequality : ウィキペディア英語版 | Landau–Kolmogorov inequality In mathematics, the Landau–Kolmogorov inequality, named after Edmund Landau and Andrey Kolmogorov, is the following family of interpolation inequalities between different derivatives of a function ''f'' defined on a subset ''T'' of the real numbers: : ==On the real line==
For ''k'' = 1, ''n'' = 2, ''T''=R the inequality was first proved by Edmund Landau with the sharp constant ''C''(2, 1, R) = 2. Following contributions by Jacques Hadamard and Georgiy Shilov, Andrey Kolmogorov found the sharp constants and arbitrary ''n'', ''k'': : where ''a''''n'' are the Favard constants.
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「Landau–Kolmogorov inequality」の詳細全文を読む
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