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Mat. Sb. (N.S.), 1970, Volume 82(124), Number 1(5), Pages 111–125 (Mi msb3439)  

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

An estimate of the dimension of the null spaces of linear superpositions

B. L. Fridman


Abstract: In this article it is proved that for continuously differentiable functions $f_1(x,y),f_2(x,y),…,f_n(x,y)$ a region $U$ of the $x$, $y$ plane can be found such that the dimension of the space of vectors $(\varphi_1(t),…,\varphi_n(t))$ for which $\sum_{i=1}^n\varphi_i(f_i(x,y))=0$ in $U$, where $\varphi_i(t)\in L_2$, either equals infinity or else does not exceed the number $(n-1)n/2$. Superpositions of the form $\sum_{i=1}^n\psi_i(f_i(x,y))$ are also shown to be closed and nowhere dense in $L_2$.
Bibliography: 3 titles.

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English version:
Mathematics of the USSR-Sbornik, 1970, 11:1, 101–114

Bibliographic databases:

UDC: 517.51
MSC: 46E20, 26B40, 46E15, 46B03
Received: 25.06.1969

Citation: B. L. Fridman, “An estimate of the dimension of the null spaces of linear superpositions”, Mat. Sb. (N.S.), 82(124):1(5) (1970), 111–125; Math. USSR-Sb., 11:1 (1970), 101–114

Citation in format AMSBIB
\Bibitem{Fri70}
\by B.~L.~Fridman
\paper An estimate of the dimension of the null spaces of linear superpositions
\jour Mat. Sb. (N.S.)
\yr 1970
\vol 82(124)
\issue 1(5)
\pages 111--125
\mathnet{http://mi.mathnet.ru/msb3439}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=264007}
\zmath{https://zbmath.org/?q=an:0197.33801|0216.09404}
\transl
\jour Math. USSR-Sb.
\yr 1970
\vol 11
\issue 1
\pages 101--114
\crossref{https://doi.org/10.1070/SM1970v011n01ABEH002064}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. B. L. Fridman, “A nowhere dense space of linear superpositions of functions of several variables”, Math. USSR-Izv., 6:4 (1972), 807–837  mathnet  crossref  mathscinet  zmath
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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