On representation by Dirichlet series of functions analytic in a halfplane

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.