SKETCH OF THE THEORY OF GROWTH OF HOLOMORPHIC FUNCTIONS IN A MULTIDIMENSIONAL TORUS

摘要

We develop an approach to the theory of growth of the class H(T~n ) of holomorphic functions in a multidimensional torus T~n based on the structure of elements of this class and well-known results of the heory of growth of entire functions of several complex variables. This approach is illustrated in the case where the growth of the function g ∈ H(T~n ) is compared with the growth of its maximum modulus on the skeleton of the polydisk. The properties of the corresponding characteristics of growth of the functions in the class H(T~n ) are studied with their relation to coefficients of the corresponding Laurent series. A comparative analysis of these results and similar assertions of the theory of growth of entire functions of several variables is given.