We denote the set
an open polydisc. We can also have polydiscs of the form
The set is called the distinguished boundary of the polydisc.
Be careful not to confuse this with the open ball in as that is defined as
When then open balls and open polydiscs are not biholomorphically equivalent (there is no 1-1 biholomorphic mapping between the two).
It is common to write for the closure of the polydisc. Be careful with this notation however as some texts outside of complex analysis use and the “disc” to represent a closed ball in two real dimensions.
Also note that when the bidisc is sometimes used.
- 1 Lars Hörmander. , North-Holland Publishing Company, New York, New York, 1973.
- 2 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
|Date of creation||2013-03-22 14:29:41|
|Last modified on||2013-03-22 14:29:41|
|Last modified by||jirka (4157)|