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Mat. Sb., 2001, Volume 192, Number 6, Pages 71–88 (Mi msb573)  

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

Impossibility of constructing continuous functions of $(n+1)$ variables from functions of $n$ variables by means of certain continuous operators

S. S. Marchenkov

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences

Abstract: Continuous functions on a unit cube are considered. The concept of continuity regulator is introduced: in the definition of uniform continuity it governs the transition “from $\varepsilon$ to $\delta$”. The problem of obtaining continuous functions of $(n+1)$ variables with continuity regulator $\delta$ variables with the same continuity regulator by means of uniformly continuous operators with continuity regulators that are superpositions of the regulator $\delta$ is posed. The insolubility of this problem is demonstrated for continuity regulators $\delta$ ($\varepsilon$) such that for each $\alpha\geqslant0$ the inequality $\delta(\varepsilon)\geqslant\varepsilon^{1+\alpha}$ holds starting from some $\varepsilon_\alpha$.

DOI: https://doi.org/10.4213/sm573

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English version:
Sbornik: Mathematics, 2001, 192:6, 863–878

Bibliographic databases:

UDC: 519.716
MSC: Primary 26B40, 26B35; Secondary 41A63, 41A30
Received: 24.08.2000

Citation: S. S. Marchenkov, “Impossibility of constructing continuous functions of $(n+1)$ variables from functions of $n$ variables by means of certain continuous operators”, Mat. Sb., 192:6 (2001), 71–88; Sb. Math., 192:6 (2001), 863–878

Citation in format AMSBIB
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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. Marchenkov S.S., “Operatory iterirovaniya na mnozhestve nepreryvnykh funktsii berovskogo prostranstva”, Vestnik Moskovskogo universiteta. Seriya 15: Vychislitelnaya matematika i kibernetika, 4 (2011), 33–37  mathscinet  zmath  elib
    2. S. S. Marchenkov, “Interpolation and Superpositions of Multivariate Continuous Functions”, Math. Notes, 93:4 (2013), 571–577  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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