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Izv. Akad. Nauk SSSR Ser. Mat., 1972, Volume 36, Issue 4, Pages 814–846 (Mi izv2336)  

This article is cited in 1 scientific paper (total in 1 paper)

A nowhere dense space of linear superpositions of functions of several variables

B. L. Fridman


Abstract: Let $\mathbf I^3$ be the unit cube of three-dimensional space $R^3$, and let $\Phi_i(x)$, $i=1,…,n$, be mappings $\Phi_i\colon\mathbf I^3\to R^2$ of class $C_2$. We prove that the set of functions $F(x)$ on $\mathbf I^3$ which can be represented in the form
$$ F(x)=\sum_{i=1}^n(\chi_i\circ\Phi_i)(x), $$
where the $\chi_i(u_1,u_2)$ are arbitrary continuous functions, $\chi_i\colon R^2\to R$, is nowhere dense in $\mathscr L_2(\mathbf I^3)$.

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English version:
Mathematics of the USSR-Izvestiya, 1972, 6:4, 807–837

Bibliographic databases:

UDC: 513.88
MSC: 26A72, 46E30
Received: 24.08.1971

Citation: B. L. Fridman, “A nowhere dense space of linear superpositions of functions of several variables”, Izv. Akad. Nauk SSSR Ser. Mat., 36:4 (1972), 814–846; Math. USSR-Izv., 6:4 (1972), 807–837

Citation in format AMSBIB
\Bibitem{Fri72}
\by B.~L.~Fridman
\paper A~nowhere dense space of linear superpositions of functions of several variables
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1972
\vol 36
\issue 4
\pages 814--846
\mathnet{http://mi.mathnet.ru/izv2336}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=318422}
\zmath{https://zbmath.org/?q=an:0253.46065}
\transl
\jour Math. USSR-Izv.
\yr 1972
\vol 6
\issue 4
\pages 807--837
\crossref{https://doi.org/10.1070/IM1972v006n04ABEH001902}


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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. G. Vitushkin, “On Hilbert's thirteenth problem and related questions”, Russian Math. Surveys, 59:1 (2004), 11–25  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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