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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 4, Pages 187–220 (Mi izv37)  

This article is cited in 4 scientific papers (total in 4 papers)

On the extension and smoothing of vector-valued functions

I. G. Tsar'kov


Abstract: Smoothing of maps in Banach spaces is considered in this article. We construct an example of an infinitely differentiable vector-valued function on a subspace $L$ in $C[0,1]$ that does not have a uniformly continuous extension to a neighbourhood of $L$. The Kolmogorov widths obtained are correct in the order of growth of three parameters.

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English version:
Izvestiya: Mathematics, 1995, 59:4, 847–879

Bibliographic databases:

MSC: 41A65
Received: 08.10.1993

Citation: I. G. Tsar'kov, “On the extension and smoothing of vector-valued functions”, Izv. RAN. Ser. Mat., 59:4 (1995), 187–220; Izv. Math., 59:4 (1995), 847–879

Citation in format AMSBIB
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\by I.~G.~Tsar'kov
\paper On the extension and smoothing of vector-valued functions
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 4
\pages 187--220
\mathnet{http://mi.mathnet.ru/izv37}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1356356}
\zmath{https://zbmath.org/?q=an:0865.41036}
\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 4
\pages 847--879
\crossref{https://doi.org/10.1070/IM1995v059n04ABEH000037}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000169556400010}


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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. Bogachev V., “Extensions of H-Lipschitzian Mappings with Infinite-Dimensional Range”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 2:3 (1999), 461–474  crossref  mathscinet  zmath  isi
    2. Brudnyi YA. Kalton N., “Polynomial Approximation on Convex Subsets of R-N”, Constr. Approx., 16:2 (2000), 161–199  crossref  mathscinet  zmath  isi
    3. I. G. Tsar'kov, “Smoothing of Hilbert-valued uniformly continuous maps”, Izv. Math., 69:4 (2005), 149–160  mathnet  crossref  crossref  mathscinet  zmath  elib
    4. I. G. Tsar'kov, “Local Smoothing of Uniformly Smooth Maps”, Funct. Anal. Appl., 40:3 (2006), 200–206  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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