Abstract:
In this article the idea of the $\Gamma$-capacity of a set in $C^n$, the analog of the idea of capacity of a set in $C^1$, is introduced. The basic result of the paper (Theorems 2 and 3) is the following: if the function $f(z,\omega)$, where $z\in C^n$, and $\omega\in C^1$, has only a finite number of zeros as a function of $\omega$ for all $z$ in some set of positive $\Gamma$-capacity, then it is the product of an entire pseudopolynomial in $\omega$ and an entire function which is never zero.
Bibliography: 12 titles.
Fulltext:
PDF file (1700 kB)
