- Polydisc
In the theory of functions of
several complex variables , a branch ofmathematics , a polydisc is aCartesian product of discs.More specifically, if we denote by the open disc of center "z" and radius "r" in the
complex plane , then an open polydisc is a set of the form:
It can be equivalently written as
:
One should not confuse the polydisc with the
open ball in Cn, which is defined as:
Here, the norm is the
Euclidean distance in Cn.When , open balls and open polydiscs are "not" biholomorphically equivalent, that is, there is no
biholomorphic mapping between the two. This was proven by Poincaré in 1907 by showing that theirautomorphism group s have different dimensions asLie group s.When the term "bidisc" is sometimes used.
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