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Mat. Sb. (N.S.), 1980, Volume 113(155), Number 1(9), Pages 3–40 (Mi msb2771)  

On uniform and asymptotic approximation on the real axis by entire functions of restricted growth

N. U. Arakelian


Abstract: This paper establishes results, including both necessary and sufficient conditions, on uniform or asymptotic approximation on the real axis, by entire functions with the slowest possible growth in the complex plane, to arbitrary continuous or continuously differentiable functions, or to functions that are holomorphic in a strip. These results generalize and improve similar results of Bernstein, Keldysh, and others.
Bibliography: 20 titles.

Full text: PDF file (1737 kB)
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English version:
Mathematics of the USSR-Sbornik, 1982, 41:1, 1–32

Bibliographic databases:

UDC: 517.53/57
MSC: Primary 30E10; Secondary 41A30
Received: 16.04.1980

Citation: N. U. Arakelian, “On uniform and asymptotic approximation on the real axis by entire functions of restricted growth”, Mat. Sb. (N.S.), 113(155):1(9) (1980), 3–40; Math. USSR-Sb., 41:1 (1982), 1–32

Citation in format AMSBIB
\Bibitem{Ara80}
\by N.~U.~Arakelian
\paper On uniform and asymptotic approximation on the real axis by entire functions of restricted growth
\jour Mat. Sb. (N.S.)
\yr 1980
\vol 113(155)
\issue 1(9)
\pages 3--40
\mathnet{http://mi.mathnet.ru/msb2771}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=590536}
\zmath{https://zbmath.org/?q=an:0478.30029|0445.30030}
\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 41
\issue 1
\pages 1--32
\crossref{https://doi.org/10.1070/SM1982v041n01ABEH002218}


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