Izvestiya. Mathematics, Tome 6 (1972) no. 4, pp. 807-837
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B. L. Fridman. A nowhere dense space of linear superpositions of functions of several variables. Izvestiya. Mathematics, Tome 6 (1972) no. 4, pp. 807-837. http://geodesic.mathdoc.fr/item/IM2_1972_6_4_a7/
@article{IM2_1972_6_4_a7,
author = {B. L. Fridman},
title = {A~nowhere dense space of linear superpositions of functions of several variables},
journal = {Izvestiya. Mathematics},
pages = {807--837},
year = {1972},
volume = {6},
number = {4},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1972_6_4_a7/}
}
TY - JOUR
AU - B. L. Fridman
TI - A nowhere dense space of linear superpositions of functions of several variables
JO - Izvestiya. Mathematics
PY - 1972
SP - 807
EP - 837
VL - 6
IS - 4
UR - http://geodesic.mathdoc.fr/item/IM2_1972_6_4_a7/
LA - en
ID - IM2_1972_6_4_a7
ER -
%0 Journal Article
%A B. L. Fridman
%T A nowhere dense space of linear superpositions of functions of several variables
%J Izvestiya. Mathematics
%D 1972
%P 807-837
%V 6
%N 4
%U http://geodesic.mathdoc.fr/item/IM2_1972_6_4_a7/
%G en
%F IM2_1972_6_4_a7
Let $\mathbf I^3$ be the unit cube of three-dimensional space $R^3$, and let $\Phi_i(x)$, $i=1,\dots,n$, 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 $\mathscr L_2(\mathbf I^3)$.
