Exceptional sets

In this paper, we study sequences of complex numbers the first order. Multiple terms are allowed for such sequences. We also consider with a finite maximum density. construct special coverings multiple sets {λk,nk} consisting circles centered at points λk radii. particular, connected components relatively small diameter, as well that C0-sets. These act exceptional entire functions exponential type. Outside these sets, obtain representation logarithm modulus an function. Previously, similar was obtained by B. Ya. Levin outside set, respect to which only its existence is asserted. contrast this, in paper present simple effective construction set. bases invariant subspace analytic convex domain. They consist linear combinations eigenfunctions and associated (exponential monomials) differentiation operator divided into groups.