This article is cited in 1 paper

On reducibility of zero sets of entire functions of several variables

A. B. Sekerin


Abstract: 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.

UDC: 517.55

Received: 01.07.1991

 English version: Siberian Mathematical Journal, 1993, 34:2, 337–346

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