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Landau–Kolmogorov inequality
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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:
: \|f^\|_ \le C(n, k, T) }^ \text 1\le k < n.
==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'':
: C(n, k, \mathbb R) = a_ a_n^~,
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)
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