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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 2012 Volume 203, Number 11, Pages 23–40 (Mi sm7910)

This article is cited 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

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.

UDC: 517.538.5+517.982.256

MSC: 41A20, 30E10

Received: 11.07.2011 and 17.04.2012

DOI: 10.4213/sm7910


 English version:
Sbornik: Mathematics, 2012, 203:11, 1553–1570

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