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 Mat. Sb. (N.S.), 1976, Volume 100(142), Number 2(6), Pages 312–334 (Mi msb2876)

On the growth of entire functions represented by regularly convergent function series

V. A. Oskolkov

Abstract: The first part of the article is devoted to the investigation of the growth of entire functions represented by the polynomial series of Abel–Goncharov and Newton, and by Taylor series with variable centering. Under certain assumptions about the sequence of interpolation nodes, we find both the order and sharp lower and upper estimates for the type of an entire function represented by an Abel–Goncharov series. Making various assumptions about the interpolation nodes, we find both the order and a sharp upper estimate for the indicator of an entire function represented by Newton's series, as well as sharp lower and upper estimates for the type of such a function.
Bibliography: 14 titles.

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English version:
Mathematics of the USSR-Sbornik, 1976, 29:2, 281–302

Bibliographic databases:

UDC: 517.535.4
MSC: 30A64, 30A80

Citation: V. A. Oskolkov, “On the growth of entire functions represented by regularly convergent function series”, Mat. Sb. (N.S.), 100(142):2(6) (1976), 312–334; Math. USSR-Sb., 29:2 (1976), 281–302

Citation in format AMSBIB
\Bibitem{Osk76} \by V.~A.~Oskolkov \paper On the growth of entire functions represented by regularly convergent function series \jour Mat. Sb. (N.S.) \yr 1976 \vol 100(142) \issue 2(6) \pages 312--334 \mathnet{http://mi.mathnet.ru/msb2876} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=409811} \zmath{https://zbmath.org/?q=an:0339.30021} \transl \jour Math. USSR-Sb. \yr 1976 \vol 29 \issue 2 \pages 281--302 \crossref{https://doi.org/10.1070/SM1976v029n02ABEH003668} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1976EZ91500011} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. V. A. Oskolkov, L. I. Kalinichenko, “Growth of entire functions represented by Dirichlet series”, Sb. Math., 187:10 (1996), 1545–1560
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