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Izv. RAN. Ser. Mat., 2004, Volume 68, Issue 3, Pages 15–28 (Mi izv484)  

This article is cited in 13 scientific papers (total in 13 papers)

On uniform approximation by $n$-analytic functions on closed sets in $\mathbb C$

A. Boivina, P. M. Gauthierb, P. V. Paramonovc

a University of Western Ontario, Department of Mathematics
b Université de Montréal
c M. V. Lomonosov Moscow State University

Abstract: Necessary and (or) sufficient conditions on a closed set $F\subset\mathbb{C}$ are given for any function $f$, continuous on $F$ and $n$-analytic on $F^0$, to be the uniform limit on $F$ of a sequence of $n$-analytic entire or $n$-analytic meromorphic functions.


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English version:
Izvestiya: Mathematics, 2004, 68:3, 447–459

Bibliographic databases:

UDC: 517.538.5+517.956.2
MSC: 30E10, 30G30
Received: 25.12.2003

Citation: A. Boivin, P. M. Gauthier, P. V. Paramonov, “On uniform approximation by $n$-analytic functions on closed sets in $\mathbb C$”, Izv. RAN. Ser. Mat., 68:3 (2004), 15–28; Izv. Math., 68:3 (2004), 447–459

Citation in format AMSBIB
\by A.~Boivin, P.~M.~Gauthier, P.~V.~Paramonov
\paper On uniform approximation by $n$-analytic functions on closed sets in~$\mathbb C$
\jour Izv. RAN. Ser. Mat.
\yr 2004
\vol 68
\issue 3
\pages 15--28
\jour Izv. Math.
\yr 2004
\vol 68
\issue 3
\pages 447--459

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    This publication is cited in the following articles:
    1. A. B. Zaitsev, “Uniform approximability of functions by polynomial solutions of second-order elliptic equations on compact plane sets”, Izv. Math., 68:6 (2004), 1143–1156  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. 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
    3. K. Yu. Fedorovskiy, “On Some Properties and Examples of Nevanlinna Domains”, Proc. Steklov Inst. Math., 253 (2006), 186–194  mathnet  crossref  mathscinet  elib
    4. J. J. Carmona, K. Yu. Fedorovskiy, “On the Dependence of Uniform Polyanalytic Polynomial Approximations on the Order of Polyanalyticity”, Math. Notes, 83:1 (2008), 31–36  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Fedorovskiy K.Yu., “Nevanlinna Domains in Problems of Polyanalytic Polynomial Approximation”, Analysis and Mathematical Physics, Trends in Mathematics, 2009, 131–142  mathscinet  zmath  isi
    6. Konstantin Yu. Fedorovskiy, “C m -Approximation by Polyanalytic Polynomials on Compact Subsets of the Complex Plane”, Complex anal oper theory, 2010  crossref  mathscinet  isi  scopus
    7. 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
    8. 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
    9. 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
    10. Proc. Steklov Inst. Math., 279 (2012), 215–229  mathnet  crossref  mathscinet  isi  elib
    11. Fedorovskiy K.Yu., “Uniform and C-M-Approximation by Polyanalytic Polynomials”, Complex Analysis and Potential Theory, CRM Proceedings & Lecture Notes, 55, eds. Boivin A., Mashreghi J., Amer Mathematical Soc, 2012, 323–329  crossref  mathscinet  zmath  isi
    12. A.D. Baranov, J.J. Carmona, K.Yu. Fedorovskiy, “Density of certain polynomial modules”, Journal of Approximation Theory, 2015  crossref  mathscinet  scopus
    13. V. I. Danchenko, “Cauchy and Poisson formulas for polyanalytic functions and applications”, Russian Math. (Iz. VUZ), 60:1 (2016), 11–21  mathnet  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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