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Matematicheskie Zametki, 2007, Volume 82, Issue 6, Pages 803–810
DOI: https://doi.org/10.4213/mzm4180 (Mi mzm4180) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Estimates of the Distances to Direct Lines and Rays from the Poles of Simplest Fractions Bounded in the Norm of $L_p$ on These Sets

P. A. Borodin

M. V. Lomonosov Moscow State University
Full-text PDF (447 kB) Citations (10)
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DOI: https://doi.org/10.4213/mzm4180
Abstract: For each $p>1$, we obtain a lower bound for the distances to the real axis from the poles of simplest fractions (i.e., logarithmic derivatives of polynomials) bounded by 1 in the norm of $L_p$ on this axis; this estimate improves the first estimate of such kind derived by Danchenko in 1994. For $p=2$, the estimate turns out to be sharp. Similar estimates are obtained for the distances from the poles of simplest fractions to the vertices of angles and rays.
Keywords: simplest fraction, logarithmic derivative, algebraic polynomial, rational function, Euler beta function, Hölder's inequality, $L_p$-norm, Hardy space.
Received: 26.12.2006
English version:
Mathematical Notes, 2007, Volume 82, Issue 6, Pages 725–732
DOI: https://doi.org/10.1134/S0001434607110168
Bibliographic databases:
UDC: 517.53
Language: Russian
Citation: P. A. Borodin, “Estimates of the Distances to Direct Lines and Rays from the Poles of Simplest Fractions Bounded in the Norm of $L_p$ on These Sets”, Mat. Zametki, 82:6 (2007), 803–810; Math. Notes, 82:6 (2007), 725–732
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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