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Izv. RAN. Ser. Mat., 2004, Volume 68, Issue 6, Pages 85–98 (Mi izv512)  

This article is cited in 5 scientific papers (total in 5 papers)

Uniform approximability of functions by polynomial solutions of second-order elliptic equations on compact plane sets

A. B. Zaitsev

Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)

Abstract: We investigate conditions for the uniform approximability of functions by polynomial solutions of second-order elliptic equations with constant complex coefficients on compact sets in $\mathbb R^2$. Some new results of a reductive nature are obtained which ensure that a compact set is an approximation compactum if certain special subsets with a simpler topological structure have this property.

DOI: https://doi.org/10.4213/im512

Full text: PDF file (1235 kB)
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English version:
Izvestiya: Mathematics, 2004, 68:6, 1143–1156

Bibliographic databases:

UDC: 517.5
MSC: 30A98, 30D40, 31A05, 31B05, 35J05, 41A10, 41A30, 42B99, 46J10, 46J25
Received: 31.05.2004

Citation: A. B. Zaitsev, “Uniform approximability of functions by polynomial solutions of second-order elliptic equations on compact plane sets”, Izv. RAN. Ser. Mat., 68:6 (2004), 85–98; Izv. Math., 68:6 (2004), 1143–1156

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. B. Zaitsev, “Uniform Approximation by Polynomial Solutions of Second-Order Elliptic Equations, and the Corresponding Dirichlet Problem”, Proc. Steklov Inst. Math., 253 (2006), 57–70  mathnet  crossref  mathscinet  elib
    2. Fedorovskiy K.Yu., “Nevanlinna Domains in Problems of Polyanalytic Polynomial Approximation”, Analysis and Mathematical Physics, Trends in Mathematics, 2009, 131–142  mathscinet  zmath  isi
    3. A. D. Baranov, K. Yu. Fedorovskiy, “Boundary regularity of Nevanlinna domains and univalent functions in model subspaces”, Sb. Math., 202:12 (2011), 1723–1740  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. K. Yu. Fedorovskiy, “On $\mathcal C^m$-approximability of functions by polynomial solutions of elliptic equations on compact plane sets”, St. Petersburg Math. J., 24:4 (2013), 677–689  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    5. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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