Pointwise estimates for the derivative of algebraic polynomials

Adrian Savchuk

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arXiv · 2104.01248

Pointwise estimates for the derivative of algebraic polynomials

Adrian Savchuk

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Abstract

We give the sufficient condition on coefficients $a_k$ of an algebraic polynomial $P(z)=\sum_{k=0}^{n}a_kz^k$, $a_n\not=0,$ for the pointwise Bernstein inequality $|P'(z)|\le n|P(z)|$ to be true for all $z\in\overline{\mathbb D}:=\{w\in\mathbb C : |w|\le 1\}$.

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Adrian Savchuk. 2021-04-02. Pointwise estimates for the derivative of algebraic polynomials. https://arxiv.org/abs/2104.01248

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