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Mat. Sb., 1997, Volume 188, Number 2, Pages 95–128 (Mi msb203)  

This article is cited in 3 scientific papers (total in 3 papers)

Haar problem for sign-sensitive approximations

E. A. Sevast'yanov

Moscow Institute of Municipal Economy and Construction

Abstract: The Haar problem for sign-sensitive approximations consists in finding necessary and sufficient conditions for a finite-dimensional subspace $L$ of the space $C(E)$ of continuous functions on a compact subset $E$ of $\mathbb R$ and a sign-sensitive weight $p(x)=(p_-(x),p_+(x))$, $x \in E$, ensuring that for each function $f$ in $L$ there exists a unique element of best approximation with weight $p$. Several conditions of this kind are established. These conditions are shown to be closely connected with the topological properties of the annihilators of the functions $p_-(x)$ and $p_+(x)$. In particular, the sign-sensitive weights $p=(p_-,p_+)$ are described such that the same condition as the one introduced by Haar for uniform approximations (that is, for $p(x) \equiv (1,1)$) serves the corresponding Haar problem.

DOI: https://doi.org/10.4213/sm203

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English version:
Sbornik: Mathematics, 1997, 188:2, 265–297

Bibliographic databases:

UDC: 517.51
MSC: 41A50, 41A52
Received: 13.09.1995

Citation: E. A. Sevast'yanov, “Haar problem for sign-sensitive approximations”, Mat. Sb., 188:2 (1997), 95–128; Sb. Math., 188:2 (1997), 265–297

Citation in format AMSBIB
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\paper Haar problem for sign-sensitive approximations
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\pages 95--128
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\issue 2
\pages 265--297
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. P. Dolzhenko, E. A. Sevast'yanov, “Approximations with a sign-sensitive weight: existence and uniqueness theorems”, Izv. Math., 62:6 (1998), 1127–1168  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. V. Pokrovskii, “The best asymmetric approximation in spaces of continuous functions”, Izv. Math., 70:4 (2006), 809–839  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Pokrovskii, AV, “Nonsymmetric approximations in spaces of continuous functions”, Doklady Mathematics, 73:2 (2006), 175  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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