We call an open set a Reinhardt domain if implies that for all real .
The reason for studying these kinds of domains is that logarithmically convex (http://planetmath.org/LogarithmicallyConvexSet) Reinhardt domain are the domains of convergence of power series in several complex variables. Note that in one complex variable, a Reinhardt domain is just a disc.
Note that the intersection of Reinhardt domains is still a Reinhardt domain, so for every Reinhardt domain, there is a smallest Reinhardt domain which contains it.
It actually turns out that a Reinhardt domain is a domain of convergence.
examples of Reinhardt domains in are polydiscs such as where is the unit disc.
- 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 14:29:37|
|Last modified on||2013-03-22 14:29:37|
|Last modified by||jirka (4157)|