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This article is cited in 8 scientific papers (total in 8 papers)
Approximation by simple partial fractions with constraints on the poles
P. A. Borodin
M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
Under various constraints on a compact subset $K$ of the complex plane $\mathbb C$ and a subset $E\subset \mathbb C$ disjoint from $K$, the problem of density in the space $AC(K)$ (the space of functions that are
continuous on a compact set $K$ and analytic in its interior) of the set of simple partial fractions (logarithmic derivatives of polynomials) with poles in $E$ is studied. The present investigation also involves examining some properties of additive subgroups of a Hilbert space.
Bibliography: 19 titles.
Keywords:
simple partial fractions, uniform approximation, restriction on the poles, additive subgroup.
DOI:
https://doi.org/10.4213/sm7910
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English version:
Sbornik: Mathematics, 2012, 203:11, 1553–1570
Bibliographic databases:
     
UDC:
517.538.5+517.982.256
MSC: 41A20, 30E10
Received: 11.07.2011 and 17.04.2012
Citation:
P. A. Borodin, “Approximation by simple partial fractions with constraints on the poles”, Mat. Sb., 203:11 (2012), 23–40; Sb. Math., 203:11 (2012), 1553–1570
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http://mi.mathnet.ru/eng/msb7910https://doi.org/10.4213/sm7910 http://mi.mathnet.ru/eng/msb/v203/i11/p23
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This publication is cited in the following articles:
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P. Chunaev, “Least deviation of logarithmic derivatives of algebraic polynomials from zero”, J. Approx. Theory, 185 (2014), 98–106
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P. A. Borodin, “Density of a semigroup in a Banach space”, Izv. Math., 78:6 (2014), 1079–1104
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A. R. Alimov, I. G. Tsar'kov, “Connectedness and other geometric properties of suns and Chebyshev sets”, J. Math. Sci., 217:6 (2016), 683–730
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P. A. Borodin, O. N. Kosukhin, “Quantitative Expressions for the Connectedness of Sets in ${\mathbb R}^n$”, Math. Notes, 98:5 (2015), 707–713
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P. A. Borodin, “Approximation by simple partial fractions with constraints on the poles. II”, Sb. Math., 207:3 (2016), 331–341
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A. R. Alimov, I. G. Tsar'kov, “Connectedness and solarity in problems of best and near-best approximation”, Russian Math. Surveys, 71:1 (2016), 1–77
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P. A. Borodin, “Approximation by sums of shifts of a single function on the circle”, Izv. Math., 81:6 (2017), 1080–1094
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V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49
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