Geodesic
A lower bound for the $L_2[-1,\,1]$-norm of the logarithmic derivative of polynomials with zeros on the unit circle
Problemy analiza, Tome 8 (2019) no. 2, pp. 67-72

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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, simplest fraction, unit circle.
Mots-clés : $C$-polynomial, norm 
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     author = {M. A. Komarov},
     title = {A lower bound for the $L_2[-1,\,1]$-norm of the logarithmic derivative of polynomials with zeros on the unit circle},
     journal = {Problemy analiza},
     pages = {67--72},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2019_8_2_a4/}
}
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M. A. Komarov. A lower bound for the $L_2[-1,\,1]$-norm of the logarithmic derivative of polynomials with zeros on the unit circle. Problemy analiza, Tome 8 (2019) no. 2, pp. 67-72. http://geodesic.mathdoc.fr/item/PA_2019_8_2_a4/