On representation by Dirichlet series of functions analytic in a~halfplane
Sbornik. Mathematics, Tome 14 (1971) no. 4, pp. 565-581
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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.
@article{SM_1971_14_4_a6,
author = {A. F. Leont'ev},
title = {On representation by {Dirichlet} series of functions analytic in a~halfplane},
journal = {Sbornik. Mathematics},
pages = {565--581},
publisher = {mathdoc},
volume = {14},
number = {4},
year = {1971},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1971_14_4_a6/}
}
A. F. Leont'ev. On representation by Dirichlet series of functions analytic in a~halfplane. Sbornik. Mathematics, Tome 14 (1971) no. 4, pp. 565-581. http://geodesic.mathdoc.fr/item/SM_1971_14_4_a6/