Hallo,

I have read about the Corona Theorem (see link:http://en.wikipedia.org/wiki/Corona_theorem). From this one ca deduce that: Let $f_{1}, ..., f_{n}$ be holomorphic bounded functions on the unit disk, which do not all simultaniously vanish. Then there exists bounded holomorphic functions $g_{1}, ..., g_{n}$ such that $\sum_{i=1}^{n}f_{i}g_{i} = 1$. My question is: is this true in several variables? Let say, if the disk is a polydisk or some open, convex ... domain?

hapchiu