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Izv. Akad. Nauk SSSR Ser. Mat., 1978, Volume 42, Issue 4, Pages 763–772 (Mi izv1790)  

This article is cited in 3 scientific papers (total in 4 papers)

On conditions for representability of entire functions by certain general series

A. F. Leont'ev, Yu. N. Frolov


Abstract: Let $f(z)$ be an entire function of order $\rho$ and $L(\lambda)$ an entire function of order $\rho_1>\rho$ with simple zeros $\lambda_1,…,\lambda_k,…$ . A series $\sum_1^\infty\alpha_kf(\lambda_kz)$ is assigned (according to a specific rule) to an arbitrary entire function $F(z)$ of order $\nu<\frac{\rho\rho_1}{\rho_1-\rho}$. Necessary and sufficient conditions on $L(\lambda)$ are found under which this series always converges to $F(z)$ in some topology.
Bibliography: 5 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1979, 13:1, 63–72

Bibliographic databases:

UDC: 517.5
MSC: 30D10
Received: 19.10.1976

Citation: A. F. Leont'ev, Yu. N. Frolov, “On conditions for representability of entire functions by certain general series”, Izv. Akad. Nauk SSSR Ser. Mat., 42:4 (1978), 763–772; Math. USSR-Izv., 13:1 (1979), 63–72

Citation in format AMSBIB
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\by A.~F.~Leont'ev, Yu.~N.~Frolov
\paper On conditions for representability of entire functions by certain general series
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1978
\vol 42
\issue 4
\pages 763--772
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\zmath{https://zbmath.org/?q=an:0425.30015|0386.30013}
\transl
\jour Math. USSR-Izv.
\yr 1979
\vol 13
\issue 1
\pages 63--72
\crossref{https://doi.org/10.1070/IM1979v013n01ABEH002011}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JB17800004}


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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. Yu. F. Korobeinik, “Representing systems”, Russian Math. Surveys, 36:1 (1981), 75–137  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. R Sandler, “Convergence of a series of exponentials associated with an entire function”, Journal of Mathematical Analysis and Applications, 117:1 (1986), 220  crossref
    3. A. G. Vitushkin, V. S. Vladimirov, A. A. Gonchar, V. V. Napalkov, S. M. Nikol'skii, A. M. Sedletskii, P. L. Ul'yanov, Yu. N. Frolov, “Aleksei Fedorovich Leont'ev (obituary)”, Russian Math. Surveys, 42:5 (1987), 145–152  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. S. N. Melikhov, “Koeffitsienty ryadov eksponent dlya analiticheskikh funktsii i operator Pomme”, Kompleksnyi analiz. Tselye funktsii i ikh primeneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 161, VINITI RAN, M., 2019, 65–103  mathnet
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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