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Mat. Sb., 2012, Volume 203, Number 11, Pages 23–40 (Mi msb7910)  

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

Full text: PDF file (573 kB)
References: PDF file   HTML file

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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    Cycle of papers

    This publication is cited in the following articles:
    1. P. Chunaev, “Least deviation of logarithmic derivatives of algebraic polynomials from zero”, J. Approx. Theory, 185 (2014), 98–106  crossref  mathscinet  zmath  isi  elib  scopus
    2. P. A. Borodin, “Density of a semigroup in a Banach space”, Izv. Math., 78:6 (2014), 1079–1104  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. 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  mathnet  crossref  mathscinet
    4. P. A. Borodin, O. N. Kosukhin, “Quantitative Expressions for the Connectedness of Sets in ${\mathbb R}^n$”, Math. Notes, 98:5 (2015), 707–713  mathnet  crossref  crossref  mathscinet  isi  elib
    5. P. A. Borodin, “Approximation by simple partial fractions with constraints on the poles. II”, Sb. Math., 207:3 (2016), 331–341  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. P. A. Borodin, “Approximation by sums of shifts of a single function on the circle”, Izv. Math., 81:6 (2017), 1080–1094  mathnet  crossref  crossref  adsnasa  isi  elib
    8. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49  mathnet
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