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- Reinhardt_domain abstract "In mathematics, especially several complex variables, an open subset of Cn is called Reinhardt domain if implies for all real numbers .The reason for studying these kinds of domains is that logarithmically convex Reinhardt domain are the domains of convergence of power series in several complex variables. Note that in one complex variable, a logarithmically convex Reinhardt domain is simply a disc.The intersection of logarithmically convex Reinhardt domains is still a logarithmically convex Reinhardt domain, so for every Reinhardt domain, there is a smallest logarithmically convex Reinhardt domain which contains it.A simple example of logarithmically convex Reinhardt domains is a polydisc, that is, a product of disks.Thullen's classical result says that a 2-dimensional bounded Reinhard domain containing the origin is biholomorphic to one of the following domains provided that the orbit of the origin by the automophism group has positive dimension:(1) (polydisc);(2) (unit ball);(3) (Thullen domain).In 1978, Toshikazu Sunada established a generalization of Thullen's result, and proved that two -dimensional bounded Reinhardt domains and are mutually biholomorphic if and only if there exists a transformation given by, being apermutation of the indices), such that .".
- Reinhardt_domain wikiPageID "21663445".
- Reinhardt_domain wikiPageRevisionID "601880724".
- Reinhardt_domain hasPhotoCollection Reinhardt_domain.
- Reinhardt_domain id "6029".
- Reinhardt_domain title "Reinhardt domain".
- Reinhardt_domain subject Category:Several_complex_variables.
- Reinhardt_domain type PhysicalEntity100001930.
- Reinhardt_domain type SeveralComplexVariables.
- Reinhardt_domain type Thing100002452.
- Reinhardt_domain type Variable109468959.
- Reinhardt_domain comment "In mathematics, especially several complex variables, an open subset of Cn is called Reinhardt domain if implies for all real numbers .The reason for studying these kinds of domains is that logarithmically convex Reinhardt domain are the domains of convergence of power series in several complex variables.".
- Reinhardt_domain label "Reinhardt domain".
- Reinhardt_domain label "Reinhardt-Gebiet".
- Reinhardt_domain sameAs Reinhardt-Gebiet.
- Reinhardt_domain sameAs m.05mqjmk.
- Reinhardt_domain sameAs Q7310358.
- Reinhardt_domain sameAs Q7310358.
- Reinhardt_domain sameAs Reinhardt_domain.
- Reinhardt_domain wasDerivedFrom Reinhardt_domain?oldid=601880724.
- Reinhardt_domain isPrimaryTopicOf Reinhardt_domain.