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Mat. Sb. (N.S.), 1983, Volume 120(162), Number 4, Pages 451–472 (Mi msb2141)  

This article is cited in 6 scientific papers (total in 6 papers)

On uniform complex approximation by lacunary polynomials

V. H. Martirosian


Abstract: Results are established on uniform approximation of functions that are continuous on compact subsets of the complex plane and holomorphic in their interiors, by lacunary polynomials whose gaps are of zero or positive density. These generalize and sharpen previous results in this direction by N. U. Arakelyan and the author. Results similar to the Walsh–Lebesgue theorem are given for lacunary polynomials, as well as an inequality for a majorant of the coefficients of the approximating polynomials.
Bibliography: 19 titles.

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English version:
Mathematics of the USSR-Sbornik, 1984, 48:2, 445–462

Bibliographic databases:

UDC: 517.53/57
MSC: 30E10
Received: 01.02.1982

Citation: V. H. Martirosian, “On uniform complex approximation by lacunary polynomials”, Mat. Sb. (N.S.), 120(162):4 (1983), 451–472; Math. USSR-Sb., 48:2 (1984), 445–462

Citation in format AMSBIB
\Bibitem{Mar83}
\by V.~H.~Martirosian
\paper On uniform complex approximation by lacunary polynomials
\jour Mat. Sb. (N.S.)
\yr 1983
\vol 120(162)
\issue 4
\pages 451--472
\mathnet{http://mi.mathnet.ru/msb2141}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=695954}
\zmath{https://zbmath.org/?q=an:0536.30028|0531.30034}
\transl
\jour Math. USSR-Sb.
\yr 1984
\vol 48
\issue 2
\pages 445--462
\crossref{https://doi.org/10.1070/SM1984v048n02ABEH002685}


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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. Wolfgang Luh, Valeri A. Martirosian, Jürgen Müller, “Universal entire functions with gap power series”, Indagationes Mathematicae, 9:4 (1998), 529  crossref
    2. Valeri A. Martirosian, Jürgen Müller, “A Liouville-type result for lacunary power series and converse results for universal holomorphic functions”, Analysis, 26:3 (2007), 393  crossref
    3. Valeri A. Martirosian, Jürgen Müller, “A Liouville-type result for lacunary power series and converse results for universal holomorphic functions”, Analysis, 26:3 (2007), 393  crossref
    4. Martirosian V.A., Mkrtchyan S.E., “On Mean Approximation by Polynomials with Gaps on Caratheodory Sets”, J. Contemp. Math. Anal.-Armen. Aca., 43:6 (2008), 372–376  crossref  mathscinet  zmath  isi
    5. T. Gharibyan, W. Luh, J. Müller, “A lacunary version of Mergelian’s approximation theorem”, Journal of Approximation Theory, 162:4 (2010), 709  crossref
    6. Martirosyan V.A. Mkrtchyan S.E., “On Mean Approximation by Polynomials with Gaps on Non-Caratheodory Domains”, J. Contemp. Math. Anal.-Armen. Aca., 45:3 (2010), 162–169  crossref  mathscinet  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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