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Matematicheskie Zametki, 2003, Volume 74, Issue 1, Pages 41–51
DOI: https://doi.org/10.4213/mzm252
(Mi mzm252)
 

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

Uniform Approximation of Functions by Polynomial Solutions to Second-Order Elliptic Equations on Compact Sets in $\mathbb{R}^2$

A. B. Zaitsev

Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)
Full-text PDF (243 kB) Citations (4)
References:
Abstract: In this paper, we study necessary and sufficient conditions for functions to be approximated uniformly on plane compact sets by polynomial solutions to second-order homogeneous elliptic equations with constant coefficients. Sufficient conditions for approximability are of reductive character, i.e., the possibility of approximating on some (simpler) parts of the compact set implies approximability on the entire compact set.
Received: 21.05.2002
English version:
Mathematical Notes, 2003, Volume 74, Issue 1, Pages 38–48
DOI: https://doi.org/10.1023/A:1025010914890
Bibliographic databases:
UDC: 517.538.5+517.956.2
Language: Russian
Citation: A. B. Zaitsev, “Uniform Approximation of Functions by Polynomial Solutions to Second-Order Elliptic Equations on Compact Sets in $\mathbb{R}^2$”, Mat. Zametki, 74:1 (2003), 41–51; Math. Notes, 74:1 (2003), 38–48
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm252
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  • 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
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