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

Проблемы анализа

Komarov M. A.¹ 

[1] Vladimir State University;

关键词: logarithmic derivative;    C-polynomial;    simplest fraction;    norm;    unit circle;   

DOI  :  10.15393/j3.art.2019.6030

来源: DOAJ

【 摘 要 】

Let C be the unit circle {z: |z| = 1} and Qn(z) bean arbitrary C-polynomial (i. e., all its zeros z1, . . ., zn ∈ C). We prove that the norm of the logarithmic derivative Q′n/Qn in the complex space L_2[−1,1] is greater than 1/8.

【 授权许可】

Unknown