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

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

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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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
2. Yu. F. Korobeinik, “Representing systems”, Math. USSR-Izv., 12:2 (1978), 309–335
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