On conditions of expandibility of analytic functions in Dirichlet series

A function $f$, analytic in $\overline D$ or analytic in $D$ and continuous in $\overline D$, where $D$ is an open bounded convex domain, is related to the well-known principle of expansion in Dirichlet series with exponents $\lambda_k$, ($k\geqslant1$) which are the zeros of an entire function of exponential type $L(\lambda)$. Necessary and sufficient conditions on $L(\lambda)$ are given which insure that the series always converges in $D$ to $f(z)$.