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Mat. Sb., 1998, Volume 189, Number 4, Pages 3–24 (Mi msb303)  

This article is cited in 9 scientific papers (total in 9 papers)

Approximation by meromorphic and entire solutions of elliptic equations in Banach spaces of distributions

A. Boivina, P. V. Paramonovb

a University of Western Ontario, Department of Mathematics
b M. V. Lomonosov Moscow State University

Abstract: For a homogeneous elliptic partial differential operator $L$ with constant coefficients and a class of functions (jet-distributions) defined on a closed, not necessarily compact, subset of $\mathbb R^n$ and belonging locally to a Banach space $V$, the approximation in the norm of $V$ of functions in this class by entire and meromorphic solutions of the equation $Lu=0$ is considered. Theorems of Runge, Mergelyan, Roth, and Arakelyan type are established for a wide class of Banach spaces $V$ and operators $L$ they encompass most of the previously considered generalizations of these theorems but also include new results.

DOI: https://doi.org/10.4213/sm303

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English version:
Sbornik: Mathematics, 1998, 189:4, 481–502

Bibliographic databases:

UDC: 517.538.5+517.956.2
MSC: 30E10, 35Jxx
Received: 23.06.1997

Citation: A. Boivin, P. V. Paramonov, “Approximation by meromorphic and entire solutions of elliptic equations in Banach spaces of distributions”, Mat. Sb., 189:4 (1998), 3–24; Sb. Math., 189:4 (1998), 481–502

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. Bonilla, A, “Lip alpha harmonic approximation on closed sets”, Proceedings of the American Mathematical Society, 129:9 (2001), 2741  crossref  mathscinet  zmath  isi
    2. J. J. Carmona, P. V. Paramonov, K. Yu. Fedorovskiy, “On uniform approximation by polyanalytic polynomials and the Dirichlet problem for bianalytic functions”, Sb. Math., 193:10 (2002), 1469–1492  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Boivin, A, “Approximation on closed sets by analytic or meromorphic solutions of elliptic equations and applications”, Canadian Journal of Mathematics-Journal Canadien de Mathematiques, 54:5 (2002), 945  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    4. A. M. Voroncov, “Joint Approximations of Distributions in Banach Spaces”, Math. Notes, 73:2 (2003), 168–182  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. A. M. Voroncov, “Estimates of $C^m$-Capacity of Compact Sets in $\mathbb{R}^N$”, Math. Notes, 75:6 (2004), 751–764  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. K. Yu. Fedorovskiy, “On Some Properties and Examples of Nevanlinna Domains”, Proc. Steklov Inst. Math., 253 (2006), 186–194  mathnet  crossref  mathscinet  elib
    7. Bernal-Gonzalez, L, “Maximal cluster sets of L-analytic functions along arbitrary curves”, Constructive Approximation, 25:2 (2007), 211  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    8. 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
    9. Paramonov P.V., Tolsa X., “On C-1-Approximability of Functions By Solutions of Second Order Elliptic Equations on Plane Compact Sets and C-Analytic Capacity”, Anal. Math. Phys., 9:3 (2019), 1133–1161  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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