Key points are not available for this paper at this time.
The theory of analytic function of several complex variables, as presented for example in the Cartan seminars First one only studies functions in polycylinders (products of open sets in the different coordinate planes). The extension of the results to more general domains is then achieved by embedding them as submanifolds of polycylinders in spaces of high dimension. The success of this procedure depends of course on the invariance of
Lars Hörmander (Fri,) studied this question.