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Izv. Akad. Nauk SSSR Ser. Mat., 1983, Volume 47, Issue 6, Pages 1224–1247 (Mi izv1461)  

On some representing systems in spaces of analytic functions

Yu. F. Korobeinik


Abstract: Let $E_\rho(z)$ be the Mittag-Leffler function. This article investigates the connection between “representing” properties for systems $\mathscr E_{\rho,\Lambda}=\{E_{\rho}(\lambda_kz)\}^{\infty}_{k=1}$ and $\mathscr E^{(n)}_{\rho,\Lambda}=\{E_\rho(\lambda_kz),zE_\rho(\lambda_kz),…,z^nE_\rho(\lambda_kz)\}^{\infty}_{k=1}$, $n\geqslant1$, as well as for systems $\mathscr E^1_{\rho,\Lambda}=\{E_\rho(\lambda_{k,1}z)\}^\infty_{k=1}$, $\mathscr E^2_{\rho,\Lambda}=\{E_\rho(\lambda_{k,2}z)\}^\infty_{k=1}$, and $\mathscr E^3_{\rho,\Lambda}=\mathscr E^1_{\rho,\Lambda}\cup\mathscr E^2_{\rho,\Lambda}$ in spaces of analytic functions.
Bibliography: 18 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1984, 23:3, 487–509

Bibliographic databases:

UDC: 517.9
MSC: Primary 30B50, 30B60, 30D10, 30D15; Secondary 46A35
Received: 25.06.1982

Citation: Yu. F. Korobeinik, “On some representing systems in spaces of analytic functions”, Izv. Akad. Nauk SSSR Ser. Mat., 47:6 (1983), 1224–1247; Math. USSR-Izv., 23:3 (1984), 487–509

Citation in format AMSBIB
\Bibitem{Kor83}
\by Yu.~F.~Korobeinik
\paper On some representing systems in spaces of analytic functions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1983
\vol 47
\issue 6
\pages 1224--1247
\mathnet{http://mi.mathnet.ru/izv1461}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=727753}
\zmath{https://zbmath.org/?q=an:0556.30004|0538.30003}
\transl
\jour Math. USSR-Izv.
\yr 1984
\vol 23
\issue 3
\pages 487--509
\crossref{https://doi.org/10.1070/IM1984v023n03ABEH001782}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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