Belonging to convergence classes of Hadamard compositions of Gelfond-Leont'ev derivatives for analytic functions

Abstract

The conditions are found, under which the belonging to Valiron convergence class of entire functions $f$ and $g$ implies the belonging to this class of Gelfond-Leont'ev derivative of Hadamard composition of functions $f$ and $g$ and of Hadamard composition of Gelfond-Leont'ev derivatives of these functions. Analogous problem is solved for analytic functions in the unit disk.