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Bernstein's Inequality

Let $P$ be a Polynomial of degree $n$ with derivative $P'$. Then

\begin{displaymath}
\vert\vert P'\vert\vert _\infty\leq n \vert\vert P\vert\vert _\infty,
\end{displaymath}

where

\begin{displaymath}
\vert\vert P\vert\vert _\infty \equiv \max_{\vert z\vert=1} \vert P(z)\vert.
\end{displaymath}




© 1996-9 Eric W. Weisstein
1999-05-26