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

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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}

$L_p$ on These Sets

P. A. Borodin

M. V. Lomonosov Moscow State University

Full-text PDF (447 kB) Citations (10)

References:

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DOI: https://doi.org/10.4213/mzm4180

Abstract: For each

p > 1

$p>1$ , 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}

$L_p$ on this axis; this estimate improves the first estimate of such kind derived by Danchenko in 1994. For

p = 2

$p=2$ , 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}

$L_p$ -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}

$L_p$ 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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Linking options:

https://www.mathnet.ru/eng/mzm4180

https://doi.org/10.4213/mzm4180

https://www.mathnet.ru/eng/mzm/v82/i6/p803

This publication is cited in the following 10 articles:

P. A. Borodin, K. S. Shklyaev, “Density of quantized approximations”, Russian Math. Surveys, 78:5 (2023), 797–851
M. A. Komarov, “Approximation by linear fractional transformations of simple partial fractions and their differences”, Russian Math. (Iz. VUZ), 62:3 (2018), 23–33
Chunaev P., Danchenko V., “Quadrature Formulas With Variable Nodes and Jackson-Nikolskii Inequalities For Rational Functions”, J. Approx. Theory, 228 (2018), 1–20
V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Extremal and approximative properties of simple partial fractions”, Russian Math. (Iz. VUZ), 62:12 (2018), 6–41
P. A. Borodin, “Density of a semigroup in a Banach space”, Izv. Math., 78:6 (2014), 1079–1104
V. I. Danchenko, “Convergence of simple partial fractions in $L_p(\mathbb R)$ ”, Sb. Math., 201:7 (2010), 985–997
V. I. Danchenko, E. N. Kondakova, “Chebyshev's alternance in the approximation of constants by simple partial fractions”, Proc. Steklov Inst. Math., 270 (2010), 80–90
V. Yu. Protasov, “Approximation by simple partial fractions and the Hilbert transform”, Izv. Math., 73:2 (2009), 333–349
P. A. Borodin, “Approximation by simple partial fractions on the semi-axis”, Sb. Math., 200:8 (2009), 1127–1148
E. N. Kondakova, “Interpolyatsiya naiprosteishimi drobyami”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 9:2 (2009), 30–37

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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