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Matematicheskie Zametki, 1997, Volume 62, Issue 3, Pages 372–382
DOI: https://doi.org/10.4213/mzm1619
(Mi mzm1619)
 

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

Approximation by harmonic functions in the Cm-Norm and harmonic Cm-capacity of compact sets in Rn

Yu. A. Gorokhov

M. V. Lomonosov Moscow State University
Full-text PDF (231 kB) Citations (4)
References:
Abstract: We study the function Λm(X), 0<m<1, of compact sets X in Rn, n2, defined as the distance in the space Cm(X)lipm(X) from the function |x|2 to the subspace Hm(X) which is the closure in Cm(X) of the class of functions harmonic in the neighborhood of X (each function in its own neighborhood). We prove the equivalence of the conditions Λm(X)=0 and Cm(X)=Hm(X). We derive an estimate from above that depends only on the geometrical properties of the set X (on its volume).
Received: 01.11.1995
English version:
Mathematical Notes, 1997, Volume 62, Issue 3, Pages 314–322
DOI: https://doi.org/10.1007/BF02360872
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: Yu. A. Gorokhov, “Approximation by harmonic functions in the Cm-Norm and harmonic Cm-capacity of compact sets in Rn”, Mat. Zametki, 62:3 (1997), 372–382; Math. Notes, 62:3 (1997), 314–322
Citation in format AMSBIB
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\by Yu.~A.~Gorokhov
\paper Approximation by harmonic functions in the $C^m$-Norm and harmonic $C^m$-capacity of compact sets in $\mathbb R^n$
\jour Mat. Zametki
\yr 1997
\vol 62
\issue 3
\pages 372--382
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\crossref{https://doi.org/10.4213/mzm1619}
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\zmath{https://zbmath.org/?q=an:0921.41010}
\transl
\jour Math. Notes
\yr 1997
\vol 62
\issue 3
\pages 314--322
\crossref{https://doi.org/10.1007/BF02360872}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000072500900006}
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  • https://www.mathnet.ru/eng/mzm1619
  • https://doi.org/10.4213/mzm1619
  • https://www.mathnet.ru/eng/mzm/v62/i3/p372
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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    References:78
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