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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Volume 298, Pages 216–226
DOI: https://doi.org/10.1134/S0371968517030141 (Mi tm3810) 		 
This article is cited in 5 scientific papers (total in 5 papers)

New Criteria for Uniform Approximability by Harmonic Functions on Compact Sets in $\mathbb R^2$

P. V. Paramonovab

a Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia
b Bauman Moscow State Technical University, Vtoraya Baumanskaya ul. 5/1, Moscow, 105005 Russia
Full-text PDF (226 kB) Citations (5)
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DOI: https://doi.org/10.1134/S0371968517030141
Abstract: New uniform approximability criteria formulated in terms of logarithmic capacity are obtained for approximations by harmonic functions on compact sets in $\mathbb R^2$. A relationship between these approximations and analogous approximations on compact sets in $\mathbb R^3$ is established.
Keywords: uniform approximation by harmonic functions, Vitushkin-type localization operator, harmonic capacity, logarithmic capacity, reduction method.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.3843.2017/4.6
The research was supported by the Ministry of Education and Science of the Russian Federation, project no. 1.3843.2017/4.6.
Received: February 6, 2017
English version:
Proceedings of the Steklov Institute of Mathematics, 2017, Volume 298, Pages 201–211
DOI: https://doi.org/10.1134/S0081543817060141
Bibliographic databases:
Document Type: Article
UDC: 517.572+517.544.5+517.982.43
Language: Russian
Citation: P. V. Paramonov, “New Criteria for Uniform Approximability by Harmonic Functions on Compact Sets in $\mathbb R^2$”, Complex analysis and its applications, Collected papers. On the occasion of the centenary of the birth of Boris Vladimirovich Shabat, 85th anniversary of the birth of Anatoliy Georgievich Vitushkin, and 85th anniversary of the birth of Andrei Aleksandrovich Gonchar, Trudy Mat. Inst. Steklova, 298, MAIK Nauka/Interperiodica, Moscow, 2017, 216–226; Proc. Steklov Inst. Math., 298 (2017), 201–211
Citation in format AMSBIB
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\paper New Criteria for Uniform Approximability by Harmonic Functions on Compact Sets in $\mathbb R^2$
\inbook Complex analysis and its applications
\bookinfo Collected papers. On the occasion of the centenary of the birth of Boris Vladimirovich Shabat, 85th anniversary of the birth of Anatoliy Georgievich Vitushkin, and 85th anniversary of the birth of Andrei Aleksandrovich Gonchar
\serial Trudy Mat. Inst. Steklova
\yr 2017
\vol 298
\pages 216--226
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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