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

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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. Paramonov^ab

^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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\yr 2017

\vol 298

\pages 216--226

\publ MAIK Nauka/Interperiodica

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Linking options:

https://www.mathnet.ru/eng/tm3810

https://doi.org/10.1134/S0371968517030141

https://www.mathnet.ru/eng/tm/v298/p216

This publication is cited in the following 5 articles:

M. Ya. Mazalov, P. V. Paramonov, K. Yu. Fedorovskiy, “Criteria for $C^m$ -approximability of functions by solutions of homogeneous second-order elliptic equations on compact subsets of $\mathbb{R}^N$ and related capacities”, Russian Math. Surveys, 79:5 (2024), 847–917
P. V. Paramonov, “On metric properties of $C$ -capacities associated with solutions of second-order strongly elliptic equations in $\pmb{\mathbb R}^2$ ”, Sb. Math., 213:6 (2022), 831–843
M. Ya. Mazalov, “Uniform approximation of functions by solutions of second order homogeneous strongly elliptic equations on compact sets in ${\mathbb{R}}^2$ ”, Izv. Math., 85:3 (2021), 421–456
P. V. Paramonov, “Uniform approximation of functions by solutions of strongly elliptic equations of second order on compact subsets of $\mathbb R^2$ ”, Sb. Math., 212:12 (2021), 1730–1745
M. Ya. Mazalov, “A criterion for uniform approximability of individual functions by solutions of second-order homogeneous elliptic equations with constant complex coefficients”, Sb. Math., 211:9 (2020), 1267–1309

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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