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Tr. Mat. Inst. Steklova, 2018, Volume 301, Pages 7–17 (Mi tm3916)  

$C^m$ approximation of functions by solutions of second-order elliptic systems on compact sets in the plane

A. O. Bagapshab, K. Yu. Fedorovskiyac

a Bauman Moscow State Technical University, Vtoraya Baumanskaya ul. 5/1, Moscow, 105005 Russia
b Dorodnicyn Computing Centre, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333 Russia
c Mathematics and Mechanics Faculty, St. Petersburg State University, Universitetskii pr. 28, Peterhof, St. Petersburg, 198504 Russia

Abstract: This paper is a brief survey of the recent results in problems of approximating functions by solutions of homogeneous elliptic systems of PDEs on compact sets in the plane in the norms of $C^m$ spaces, $m\geq0$. We focus on general second-order systems. For such systems the paper complements the recent survey by M. Mazalov, P. Paramonov, and K. Fedorovskiy (2012), where the problems of $C^m$ approximation of functions by holomorphic, harmonic, and polyanalytic functions as well as by solutions of homogeneous elliptic PDEs with constant complex coefficients were considered.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.517.2016/1.4
1.3843.2017/4.6
Russian Foundation for Basic Research 16-01-00781
18-01-00764
Simons Foundation Simons-IUM fellowship
The research was supported by the Ministry of Education and Science of the Russian Federation (project nos. 1.517.2016/1.4 (second author) and 1.3843.2017/4.6) and by the Russian Foundation for Basic Research (project nos. 16-01-00781 and 18-01-00764). The second author was also supported by the Simons Foundation (Simons–IUM fellowship).


DOI: https://doi.org/10.1134/S0371968518020012

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English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 301, 1–10

Bibliographic databases:

UDC: 517.53
Received: January 31, 2018

Citation: A. O. Bagapsh, K. Yu. Fedorovskiy, “$C^m$ approximation of functions by solutions of second-order elliptic systems on compact sets in the plane”, Complex analysis, mathematical physics, and applications, Collected papers, Tr. Mat. Inst. Steklova, 301, MAIK Nauka/Interperiodica, Moscow, 2018, 7–17; Proc. Steklov Inst. Math., 301 (2018), 1–10

Citation in format AMSBIB
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\by A.~O.~Bagapsh, K.~Yu.~Fedorovskiy
\paper $C^m$ approximation of functions by solutions of second-order elliptic systems on compact sets in the plane
\inbook Complex analysis, mathematical physics, and applications
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2018
\vol 301
\pages 7--17
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3916}
\crossref{https://doi.org/10.1134/S0371968518020012}
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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