Minimal absolutely representing systems of exponential functions in spaces of analytic functions with given boundary smoothness

We consider spaces of functions holomorphic in a convex domain which are infinitely differentiable up to the boundary and have certain estimates of all derivatives. Some necessary and sufficient conditions are obtained for a minimal system of exponential functions to be an absolutely representing system in the spaces which are generated by a single weight. Relying on these results, we prove that absolutely representing systems of exponentials do not have the stability property under the passage to the limit over domains.