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

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

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.

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Veröffentlicht in:Issues of analysis 2019-06, Vol.26 (2), p.67-72
1. Verfasser: Komarov, M. A.
Format: Artikel
Sprache:eng
Schlagworte:
C-polynomial
logarithmic derivative
norm
simplest fraction
unit circle
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Zusammenfassung: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.
ISSN:2306-3432
2306-3424
2306-3432
DOI:10.15393/j3.art.2019.6030