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A Generalization of A Theorem of Paul Turan
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If P(z) is a polynomial of degree n, then
Max|z|=1 |P(z)| ≤ n Max |z|=1 |P(z)|.
In (1) equality holds if and only if P[z) has all its zeros at the origin. Inequality (1) is an immediate consequence of S.Bernstein's theorem on the derivative of a Trigonometric Polynomial. (For reference see [2]).
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