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Sbornik: Mathematics, 2012, Volume 203, Issue 11, Pages 1553–1570
DOI: https://doi.org/10.1070/SM2012v203n11ABEH004275 (Mi sm7910) 		 
This article is cited in 11 scientific papers (total in 11 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
English version PDF (469 kB) Citations (11)
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DOI: https://doi.org/10.1070/SM2012v203n11ABEH004275
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.
Received: 11.07.2011 and 17.04.2012
Russian version:
Matematicheskii Sbornik, 2012, Volume 203, Number 11, Pages 23–40
DOI: https://doi.org/10.4213/sm7910
Bibliographic databases:
Document Type: Article
UDC: 517.538.5+517.982.256
MSC: 41A20, 30E10
Language: English
Original paper language: Russian
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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    This publication is cited in the following 11 articles:
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    Abstract page:836
    Russian version PDF:309
    English version PDF:26
    References:131
    First page:69
     
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