Division of holomorphic functions and growth conditions
Division of holomorphic functions and growth conditions
Let $D$ be a strictly convex domain of $\mathbb{C}^{n}$, $f_{1}$ and $f_{2}$ be two holomorphic functions defined on a neighbourhood of $\overline{D}$ and set $X_{l}=\{z,f_{l}(z)=0\}$, $l=1,2$. Suppose that $X_{l}\cap bD$ is transverse for $l=1$ and $l=2$, and that $X_{1}\cap X_{2}$ is a complete intersection. We give necessary conditions when $n\geq2$ …