This article is cited in 10 papers

On convergence conditions for Dirichlet series on closed polygons

V. K. Dzyadyk


Abstract: This paper treats the questions of convergence and summability on a convex polygon $Q$ of the Dirichlet series of a function $f(z)$ which is analytic in $Q$ and continuous on $\overline Q$. Necessary and sufficient conditions for convergence are given for the case of a square; in the general case, if the necessary conditions for convergence are satisfied, it is sufficient that the integral $\int_0^1\frac{\omega(f;t)}t\,dt$ converge.
Bibliography: 7 titles.

UDC: 517.522.6

MSC: Primary 30A16; Secondary 30A82

Received: 18.10.1973

 English version: Mathematics of the USSR-Sbornik, 1974, 24:4, 463–481

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