Coefficients of Exponential Series for Analytic Functions and the Pommiez Operator

In this paper, we present results of the existence a linear continuous right inverse operator for representation analytic functions in bounded convex domain complex plane by series quasi-polynomials and exponentials. We also closely related on A. F. Leontiev interpolating function and, more generally, functional corresponding Pommiez operator. examine cyclic vectors closed invariant subspaces weighted spaces entire functions.