Domain, double-circled
From Encyclopedia of Mathematics
A domain 
in the two-dimensional complex space 
having the following property: There is a point 
such that, with each point 
, all points 
with coordinates
 |
belong to 
. The point 
is said to be the centre of the double-circled domain. If a double-circled domain contains its own centre, it is said to be complete; if it does not, it is called incomplete. Examples of complete double-circled domains are a sphere or a bicylinder; examples of an incomplete double-circled domain include the Cartesian product of annuli. An 
-circled domain, or a Reinhardt domain, is defined in a similar manner.
Comments
References
| [a1] | L. Hörmander, "An introduction to complex analysis in several variables" , North-Holland (1973) pp. Chapt. 2.4 |
How to Cite This Entry:
Domain, double-circled. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Domain,_double-circled&oldid=11787
Domain, double-circled. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Domain,_double-circled&oldid=11787
This article was adapted from an original article by M. Shirinbekov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article