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 Lp 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.
Citation:
P. A. Borodin, “Estimates of the Distances to Direct Lines and Rays from the Poles of Simplest Fractions Bounded in the Norm of Lp on These Sets”, Mat. Zametki, 82:6 (2007), 803–810; Math. Notes, 82:6 (2007), 725–732
\Bibitem{Bor07}
\by P.~A.~Borodin
\paper 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
\jour Mat. Zametki
\yr 2007
\vol 82
\issue 6
\pages 803--810
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\jour Math. Notes
\yr 2007
\vol 82
\issue 6
\pages 725--732
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https://doi.org/10.4213/mzm4180
https://www.mathnet.ru/eng/mzm/v82/i6/p803
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