Про дію диференціального виразу нескінченного порядку в класах цілих функцій багатьох комплексних змінних

Abstract

We investigate the action of the partial differential expression L(∂/∂z) of infinite order generally with constant coefficients, whose symbol is an entire function L(λ) of several complex variables, onto an entire function f(z), z О Cn. We specify the conditions on growth orders by the set of variables of the entire functions L(λ) and f(z) providing the expression's action to be correct. We clarify also the growth order of the result of the expression's action as an entire function by the set of variables.