On discrete weakly sufficient sets in certain spaces of entire functions

This article contains a study of weakly sufficient sets in a certain space of entire functions of exponential type. The following is a consequence of the results obtained: If $D$ is an infinite convex domain, then there exists a system $\{\lambda_k\}_{k=1}^\infty$ (which is minimal in a certain sense) such that any analytic function in $D$ can be represented by a series of the form $\sum a_k\exp\lambda_kz$. For bounded convex domains an analogous result was obtained previously by Leont'ev.
Bibliography: 10 titles.