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Mat. Sb., 1996, Volume 187, Number 5, Pages 3–14 (Mi msb125)  

This article is cited in 2 scientific papers (total in 3 papers)

Existence of the best possible uniform approximation of a function of several variables by a sum of functions of fewer variables

A. L. Garkavia, V. A. Medvedeva, S. Ya. Havinson

a Moscow State University of Civil Engineering

Abstract: Let $\varphi_i$ be some maps of a set $X$ onto sets $i=1,…,n$, $n\geqslant 2$. Approximations of real function $f$ on $X$ by sums $g_1\circ \varphi _1+…+g_n\circ \varphi _n$ are considered, where the $g_i$ are real function on $X_i$. Under certain constraints on the $\varphi_i$ the existence of the best possible approximation is proved in three cases. In the first case the function $f$ and the approximating sums are bounded, but the functions $\varphi_i$ can be unbounded. In the second case $f$ and the $g_i$ are bounded. In the third case $f$ and the $g_i$ are continuous, $X$ and the $X_i$ are compact sets with metrics, and the maps $\varphi_i$ are continuous.

DOI: https://doi.org/10.4213/sm125

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English version:
Sbornik: Mathematics, 1996, 187:5, 623–634

Bibliographic databases:

UDC: 517.5
MSC: Primary 41A50; Secondary 26B40
Received: 22.12.1994

Citation: A. L. Garkavi, V. A. Medvedev, S. Ya. Havinson, “Existence of the best possible uniform approximation of a function of several variables by a sum of functions of fewer variables”, Mat. Sb., 187:5 (1996), 3–14; Sb. Math., 187:5 (1996), 623–634

Citation in format AMSBIB
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\paper Existence of the~best possible uniform approximation of a~function of several variables by a~sum of functions of fewer variables
\jour Mat. Sb.
\yr 1996
\vol 187
\issue 5
\pages 3--14
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\pages 623--634
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    2. Ismailov, VE, “On the approximation by compositions of fixed multivariate functions with univariate functions”, Studia Mathematica, 183:2 (2007), 117  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    3. S. V. Konyagin, A. A. Kuleshov, V. E. Maiorov, “Some problems in the theory of ridge functions”, Proc. Steklov Inst. Math., 301 (2018), 144–169  mathnet  crossref  crossref  mathscinet  isi  elib  elib
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