RUS  ENG
Full version
JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2007 Volume 82, Issue 6, Pages 803–810 (Mi mzm4180)

This article is cited 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

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.

UDC: 517.53

Received: 26.12.2006

DOI: 10.4213/mzm4180


 English version:
Mathematical Notes, 2007, 82:6, 725–732

Bibliographic databases:


© Steklov Math. Inst. of RAS, 2025