Coefficients of exponential series for analytic functions and the Pommiez operator

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