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Funktsional. Anal. i Prilozhen., 2006, Volume 40, Issue 3, Pages 44–52 (Mi faa742)  

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

Local Smoothing of Uniformly Smooth Maps

I. G. Tsar'kov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We solve the problem on the uniform approximation of uniformly continuous (smooth) maps by maps having the maximum possible local and uniform smoothness. In particular, we prove that each uniformly continuous map of the Hilbert space $l_2$ into itself can be approximated by locally infinitely differentiable maps having a Lipschitz derivative.

Keywords: approximation, smoothing, local smoothness, uniform smoothness, Lipschitz derivative

DOI: https://doi.org/10.4213/faa742

Full text: PDF file (196 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2006, 40:3, 200–206

Bibliographic databases:

UDC: 517.17
Received: 30.11.2004

Citation: I. G. Tsar'kov, “Local Smoothing of Uniformly Smooth Maps”, Funktsional. Anal. i Prilozhen., 40:3 (2006), 44–52; Funct. Anal. Appl., 40:3 (2006), 200–206

Citation in format AMSBIB
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\by I.~G.~Tsar'kov
\paper Local Smoothing of Uniformly Smooth Maps
\jour Funktsional. Anal. i Prilozhen.
\yr 2006
\vol 40
\issue 3
\pages 44--52
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\jour Funct. Anal. Appl.
\yr 2006
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  • https://doi.org/10.4213/faa742
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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. I. G. Tsar'kov, “Local and global continuous $\varepsilon$-selection”, Izv. Math., 80:2 (2016), 442–461  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Tsar'kov I.G., “Smoothing of Real-Valued Functions on Uniformly Smooth Spaces”, Russ. J. Math. Phys., 25:3 (2018), 409–414  crossref  mathscinet  zmath  isi  scopus
    3. I. G. Tsar'kov, “Weakly monotone sets and continuous selection from a near-best approximation operator”, Proc. Steklov Inst. Math., 303 (2018), 227–238  mathnet  crossref  crossref  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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