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Bernstein's inequality

In the mathematical theory of functional analysis, Bernstein's inequality is defined as follows.

Let P be a polynomial of degree n with derivative P′. Then

\max(P') \le n\cdot\max(P)

where we define

\max(X) \equiv \max_{|z| \leq 1} \big|X(z)\big|.

The inequality is named after Sergei Natanovich Bernstein and finds uses in the field of approximation theory.

Last updated: 05-29-2005 11:10:38
Science Fair Project Encyclopedia Contents Page
10-26-2009 08:16:03
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