On A. F. Leont'ev's interpolating function

Abstract

We introduce and study an abstract version of an interpolating functional. It is defined by means of Pommiez operator acting in an countable inductive limit of weighted Fréchet spaces of entire functions and of an entire function of two complex variables. The properties of the corresponding Pommiez operator are studied. The A. F. Leont'ev's interpolating function used widely in the theory of exponentional series and convolution operators and as well as the interpolating functional applied earlier for solving the problem on the existence of a continuous linear right inverse to the operator of representation of analytic functions on a bounded convex domain in $\mathrm C$ by quasipolynomial series are partial cases of the introduced interpolating functional.