Extensions of the class of entire functions of several variables and related topics

The object of the study is the class of holomorphic functions in a multidimensional toric space. We distinguish the subclass of the functions equivalent to entire functions in the following sense: $g$ belongs to the subclass whenever there exists a monomial holomorphic mapping $\mathscr F$ such that $f=g\circ\mathscr F$ is an entire function. We give a full description of the functions of the subclass under consideration in terms of the geometric properties of the supports of the series they expand in. For the appearing extensions of the class of entire functions of several variables, we develop an approach to constructing a growth theory for these classes. Applying the method, we find a multidimensional analog to the expansion of a holomorphic function in a Laurent series.