Completeness of exponential systems in spaces of functions on a ray and the Korenblum–Seip's characteristic

Let $\{\lambda_k\}$ be a sequence of points in the right half-plane of the complex plane.We give sufficient conditions of completeness of the exponential system $\{e^{-\lambda_kx}\}$ in a weighted space of functions which are integrable on the positive semiaxis with a power weight in the terms of the Korenblum–Seip's characteristic. The characteristic was arisen from a description of duistribution of zero sets for functions from uniform Bergman spaces in the unit disk.