Completeness criteria of an exponential system in geometric terms of breadth in the direction

In this paper, we establish criterions for the completeness of an exponential system in spaces of functions that are continuous on a convex compact set and holomorphic in the interior of this compact set and in spaces of holomorphic functions in a convex domain in terms of the directional width of a compact set or a domain. The main results are formulated exclusively in terms of the relationship between the breadth in the direction or the diameter of a compact set or a domain, on the one hand, and the so-called logarithmic submeasures or logarithmic block densities of the distribution of exponential system indicators, on the other hand.