Zero sets for classes of entire functions and a~representation of meromorphic functions

B. N. Khabibullin

Matematičeskie zametki, Tome 59 (1996) no. 4, pp. 611-617

Résumé

Let $M$ be a continuous real-valued function on $\mathbb C^n$, $n\ge1$, and let $E(M)$ be the class of entire functions $f$ on $\mathbb C^n$ such that $\log|f|\le M$. We give a dual statement for the problem of the description of zero sets of functions in $E(M)$ and the possibility of representing functions $f$ meromorphic on $\mathbb C^n$ by ratios $f=g/h$, where $g$ and $h$ are entire functions belonging to $E(M)$ and coprime at each point $z\in\mathbb C^n$. The dual approach suggested in the paper is new even for the case $n=1$.