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Mat. Sb., 2004, Volume 195, Number 5, Pages 79–102 (Mi msb822)  

This article is cited in 12 scientific papers (total in 12 papers)

Uniform approximations by bianalytic functions on arbitrary compact subsets of $\mathbb C$

M. Ya. Mazalov

Military Academy of Air Defence Forces of Russia Federation

Abstract: Each continuous function on an arbitrary compact subset $X$ of $\mathbb C$ that is bianalytic in the interior of $X$ is proved to be uniformly approximable on $X$ by functions bianalytic in neighbourhoods of $X$.

DOI: https://doi.org/10.4213/sm822

Full text: PDF file (391 kB)
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English version:
Sbornik: Mathematics, 2004, 195:5, 687–709

Bibliographic databases:

UDC: 517.538.5+517.956.2
MSC: 30E10, 31A30
Received: 20.10.2003

Citation: M. Ya. Mazalov, “Uniform approximations by bianalytic functions on arbitrary compact subsets of $\mathbb C$”, Mat. Sb., 195:5 (2004), 79–102; Sb. Math., 195:5 (2004), 687–709

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. Ya. Mazalov, “A criterion for uniform approximability on arbitrary compact sets for solutions of elliptic equations”, Sb. Math., 199:1 (2008), 13–44  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. M. Ya. Mazalov, “Uniform approximation problem for harmonic functions”, St. Petersburg Math. J., 23:4 (2012), 731–759  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    3. 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
    4. M. Ya. Mazalov, “Criterion of uniform approximability by harmonic functions on compact sets in $\mathbb R^3$”, Proc. Steklov Inst. Math., 279 (2012), 110–154  mathnet  crossref  mathscinet  isi  elib
    5. Josep Carmona J., Cufi J., “The Calculation of the l (2)-Norm of the Index of a Plane Curve and Related Formulas”, J. Anal. Math., 120 (2013), 225–253  crossref  mathscinet  zmath  isi
    6. M. Ya. Mazalov, P. V. Paramonov, “Criteria for $C^m$-approximability by bianalytic functions on planar compact sets”, Sb. Math., 206:2 (2015), 242–281  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. A.D. Baranov, J.J. Carmona, K.Yu. Fedorovskiy, “Density of certain polynomial modules”, Journal of Approximation Theory, 2015  crossref  mathscinet
    8. V. I. Danchenko, “Cauchy and Poisson formulas for polyanalytic functions and applications”, Russian Math. (Iz. VUZ), 60:1 (2016), 11–21  mathnet  crossref  isi
    9. Fedorovskiy K.Yu., “Two Problems on Approximation By Solutions of Elliptic Systems on Compact Sets in the Plane”, Complex Var. Elliptic Equ., 63:7-8, SI (2018), 961–975  crossref  mathscinet  zmath  isi  scopus
    10. M. Ya. Mazalov, “On Bianalytic Capacities”, Math. Notes, 103:4 (2018), 672–677  mathnet  crossref  crossref  isi  elib
    11. A. O. Bagapsh, K. Yu. Fedorovskiy, “$C^m$ approximation of functions by solutions of second-order elliptic systems on compact sets in the plane”, Proc. Steklov Inst. Math., 301 (2018), 1–10  mathnet  crossref  crossref  isi  elib
    12. Yang L., “Bounded Point Evaluations For Certain Polynomial and Rational Modules”, J. Math. Anal. Appl., 474:1 (2019), 219–241  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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