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Mat. Sb. (N.S.), 1971, Volume 85(127), Number 4(8), Pages 563–580 (Mi msb3278)  

This article is cited in 1 scientific paper (total in 2 paper)

On representation by Dirichlet series of functions analytic in a halfplane

A. F. Leont'ev


Abstract: The author has proved (RZhMat., 1969, 12B169) that every entire function can be represented by a Dirichlet series in the complex plane. In a more recent paper (Mat. Sb. (N.S.) 81(123) (1970), 552–579) he proved that if $D$ is a bounded open convex domain, then every function analytic in $D$ can be represented in $D$ by a Dirichlet series. This left open the question of the possible representation by Dirichlet series of functions analytic in an unbounded convex domain other than the entire plane, for example, a halfplane. Here it is proved that if $D$ is an unbounded open convex domain whose boundary consists of a finite number of line segments (for example, a halfplane, angle, or strip), then every function analytic in $D$ can be represented in $D$ by a Dirichlet series.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Sbornik, 1971, 14:4, 565–581

Bibliographic databases:

UDC: 517.53
MSC: 30A16
Received: 15.10.1970

Citation: A. F. Leont'ev, “On representation by Dirichlet series of functions analytic in a halfplane”, Mat. Sb. (N.S.), 85(127):4(8) (1971), 563–580; Math. USSR-Sb., 14:4 (1971), 565–581

Citation in format AMSBIB
\Bibitem{Leo71}
\by A.~F.~Leont'ev
\paper On representation by Dirichlet series of functions analytic in a~halfplane
\jour Mat. Sb. (N.S.)
\yr 1971
\vol 85(127)
\issue 4(8)
\pages 563--580
\mathnet{http://mi.mathnet.ru/msb3278}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=304622}
\zmath{https://zbmath.org/?q=an:0225.30005}
\transl
\jour Math. USSR-Sb.
\yr 1971
\vol 14
\issue 4
\pages 565--581
\crossref{https://doi.org/10.1070/SM1971v014n04ABEH002821}


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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. V. S. Vladimirov, S. M. Nikol'skii, Yu. N. Frolov, “Aleksei Fedorovich Leont'ev (on his sixtieth birthday)”, Russian Math. Surveys, 32:3 (1977), 131–144  mathnet  crossref  mathscinet  zmath
    2. Yu. F. Korobeinik, “Representing systems”, Math. USSR-Izv., 12:2 (1978), 309–335  mathnet  crossref  mathscinet  zmath
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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