On reducibility of zero sets of entire functions of several variables

In the article is given a necessary and sufficient condition for a plurisubharmonic function to be representable as the integral whose kernel is the logarithm of the modulus of a holomorphic polynomial of a fixed degree. The indicated condition is formulated in terms of the properties of the Radon transform. Grounding on this result, the article establishes a necessary and sufficient condition for an entire function of several variables to be presentable as an infinite product of polynomials whose degrees do not exceed a fixed number.