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

O. M. Mulyava, M. M. Sheremeta


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.

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