Completeness of exponential systemsin function spaces in terms of area

In this paper, we establish completeness conditions for exponential systems in spaces of functions that are continuous on a compact set with connected complement and holomorphic inside this compact set, in spaces of holomorphic functions in a bounded simply connected domain in terms of the Euclidean area of the convex hull of this compact set or a domain and in terms of some special characteristics or distribution densities of the exponents of the exponential system.