ON REPRESENTATION BY DIRICHLET SERIES OF FUNCTIONS ANALYTIC IN A HALFPLANE

Abstract

The author has proved (MR 41 #471) that every entire function can be represented by a Dirichlet series in the complex plane. In a more recent paper (MR 41 #5604) 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 items.