This article is cited in 4 papers

A lower bound for the $L_2[-1,\,1]$-norm of the logarithmic derivative of polynomials with zeros on the unit circle

M. A. Komarov

Vladimir State University, Gor'kogo street 87, Vladimir 600000, Russia

Abstract: Let $C$ be the unit circle $\{z:|z|=1\}$ and $Q_n(z)$ be an arbitrary $C$-polynomial (i.e., all its zeros $z_1,\dots, z_n\in C$). We prove that the norm of the logarithmic derivative $Q_n'/Q_n$ in the complex space $L_2[-1, 1]$ is greater than $1/8$.

Keywords: logarithmic derivative, $C$-polynomial, simplest fraction, norm, unit circle.

UDC: 517.538.5

MSC: 41A20, 41A29

Received: 28.02.2019
Revised: 20.05.2019
Accepted: 20.05.2019

Language: English

DOI: 10.15393/j3.art.2019.6030

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