I asked to some professors of my university and no one was able to help me (the one who held the course is abroad for a period, otherwise I'd ask him, obviously).
My problem is that simply I don't understand the first sentence of the proof of Theorem 1.5.3 (you can see below) at all:
- Thesis is: $f\in\operatorname{hol}(\Delta\times\Delta)$: why from proving $f$ is holomorphic on every relatively compact polydisc should the thesis follows?
- What is a relatively compact polydisk?
- In which space are there polydisks relatively compact?
- Why does since we have to prove that $f$ is holomorphic on every relatively compact polydisc imply that we can take $f$ holomorphic on a strip slightly bigger than $\Delta\times\Delta_{\varepsilon}$ (morover: I think a slightly bigger strip is $\Delta_{1+\delta}\times\Delta_{\delta+\varepsilon}$, for some $\delta>0$: is this correct?).
If you can help me to shade some light on it I would be very grateful. I'm going crary about this. Many many thanks.
EDIT In order to be clearer, I'm posting some more material, hoping someone can help.
