On the growth of polynomials

Dryanov, D.; Rahman, Q.

doi:10.1090/S0002-9939-98-04227-0

On the growth of polynomials
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by D. Dryanov and Q. I. Rahman PDF

Proc. Amer. Math. Soc. 126 (1998), 1415-1423 Request permission

Abstract:

Let $f$ be a polynomial of degree $n$ having only real zeros and none in $(-1,1)$. We look for a sharp upper bound for $|f(z)|$ at an arbitrary point of the complex plane ${\mathbb {C}}$ in terms of the supremum norm on $[-1,1]$.

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