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.

 

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