SOME QUESTIONS ON THE DISTRIBUTION OF ZEROS OF ENTIRE FUNCTIONS OF SEVERAL VARIABLES

Abstract

In this article the idea of the ?-capacity of a set in Cn, the analog of the idea of capacity of a set in C1, is introduced. The basic result of the paper (Theorems 2 and 3) is the following: if the function f(z, w), where z Cn, and w C1, has only a finite number of zeros as a function of w for all z in some set of positive ?-capacity, then it is the product of an entire pseudopolynomial in w and an entire function which is never zero. Bibliography: 12 titles.