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Mat. Zametki, 1998, Volume 64, Issue 3, Pages 323–340 (Mi mz1403)  

This article is cited in 2 scientific papers (total in 2 papers)

The best approximation to a class of functions of several variables by another class and related extremum problems

V. V. Arestov

Ural State University

Abstract: We study the relationship between several extremum problems for unbounded linear operators of convolution type in the spaces $L_\gamma=L_\gamma(\mathbb R^m)$, $m\ge1$, $1\le\gamma\le\infty$. For the problem of calculating the modulus of continuity of the convolution operator $A$ on the function class $Q$ defined by a similar operator and for the Stechkin problem on the best approximation of the operator $A$ on the class $Q$ by bounded linear operators, we construct dual problems in dual spaces, which are the problems on, respectively, the best and the worst approximation to a class of functions by another class.

DOI: https://doi.org/10.4213/mzm1403

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English version:
Mathematical Notes, 1998, 64:3, 279–294

Bibliographic databases:

UDC: 517.518+517.983
Received: 01.09.1997

Citation: V. V. Arestov, “The best approximation to a class of functions of several variables by another class and related extremum problems”, Mat. Zametki, 64:3 (1998), 323–340; Math. Notes, 64:3 (1998), 279–294

Citation in format AMSBIB
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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. A. A. Koshelev, “The Landau–Kolmogorov problem for the Laplace operator on a ball”, Russian Math. (Iz. VUZ), 60:2 (2016), 25–32  mathnet  crossref  isi
    2. Babenko V., Babenko Yu., Kriachko N., “Inequalities of Hardy–Littlewood–Polya type for functions of operators and their applications”, J. Math. Anal. Appl., 444:1 (2016), 512–526  crossref  mathscinet  zmath  isi  elib  scopus
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