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Russian Mathematical Surveys, 2012, Volume 67, Issue 6, Pages 1023–1068
DOI: https://doi.org/10.1070/RM2012v067n06ABEH004817 (Mi rm9498) 		 
This article is cited in 34 scientific papers (total in 34 papers)

Conditions for $C^m$-approximability of functions by solutions of elliptic equations

M. Ya. Mazalova, P. V. Paramonovb, K. Yu. Fedorovskiyc

a Smolensk Branch of the Moscow Power Engineering Institute
b Moscow State University
c Bauman Moscow State Technical University
English version PDF (945 kB) Citations (34) Russian version article
References:
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DOI: https://doi.org/10.1070/RM2012v067n06ABEH004817
Abstract: This paper is a survey of results obtained over the past 20–30 years in the qualitative theory of approximation of functions by holomorphic, harmonic, and polyanalytic functions (and, in particular, by corresponding polynomials) in the norms of Whitney-type spaces $C^m$ on compact subsets of Euclidean spaces.
Bibliography: 120 titles.
Keywords: $C^m$-approximation by holomorphic, harmonic, and polyanalytic functions; $C^m$-analytic and $C^m$-harmonic capacity; $s$-dimensional Hausdorff content; Vitushkin localization operator; Nevanlinna domains; Dirichlet problem.
Received: 18.10.2012
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: Primary 30E10; Secondary 31A05, 31A30, 31A35, 30C20
Language: English
Original paper language: Russian
Citation: M. Ya. Mazalov, P. V. Paramonov, K. Yu. Fedorovskiy, “Conditions for $C^m$-approximability of functions by solutions of elliptic equations”, Russian Math. Surveys, 67:6 (2012), 1023–1068
Citation in format AMSBIB
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\by M.~Ya.~Mazalov, P.~V.~Paramonov, K.~Yu.~Fedorovskiy
\paper Conditions for $C^m$-approximability of functions by solutions of elliptic equations
\jour Russian Math. Surveys
\yr 2012
\vol 67
\issue 6
\pages 1023--1068
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  • https://www.mathnet.ru/eng/rm/v67/i6/p53
    • This publication is cited in the following 34 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:1023
    Russian version PDF:280
    English version PDF:31
    References:126
    First page:52
     
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