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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 Bernstein's theorem (polynomials) ： ウィキペディア英語版 Bernstein's theorem (polynomials) Bernstein's theorem is an inequality relating the maximum modulus of a complex polynomial function on the unit disk with the maximum modulus of its derivative on the unit disk. It was proven by Sergei Bernstein while he was working on approximation theory.〔Inequalities for the derivatives of polynomials, R.P. Boas, JR., Northwestern University, MATHEMATICS MAGAZINE, Vol. 42, No. 4, September 1969〕 == Statement == Let $\backslash max\_\; |f(z)|$ denote the maximum modulus of an arbitrary function ''f''(''z'') on |''z''| = 1, and let ''f''′(''z'') denote it's derivative. Then for every polynomial ''P''(''z'') of degree ''n'' we have : $\backslash max\_\; |P\text{'}(z)|\; \backslash le\; n\; \backslash max\_\; |P(z)|.$ The inequality is best possible with equality holding if and only if : $P(z)\; =\; \backslash alpha\; z^n,\backslash \; |\backslash alpha|\; =\; \backslash max\_\; |P(z)|.$ 〔M.A. Malik, M.C. Vong, Inequalities concerning the derivative of a polynomial Rendiconti Del Circolo Matematico Di Palermo, Serie II, Tomo XXXIV(1985), 422–426.〕 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「Bernstein's theorem (polynomials)」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.