翻訳と辞書 Words near each other ・ Reinhold von Buxhoeveden ・ Reinhold von Hoven ・ Reinhold von Werner ・ Reinhold Weege ・ Reinhold Weiss ・ Reinhold Wosab ・ Reinhardsbrunn (Verwaltungsgemeinschaft) ・ Reinhardshagen ・ Reinhardsmunster ・ Reinhardstein Castle ・ Reinhardswald ・ Reinhardt ・ Reinhardt (surname) ・ Reinhardt Canyon ・ Reinhardt cardinal ・ Reinhardt domain ・ Reinhardt Erwee ・ Reinhardt Grossmann ・ Reinhardt J. Keppler ・ Reinhardt Kristensen ・ Reinhardt Mills ・ Reinhardt Rahr ・ Reinhardt Strydom ・ Reinhardt University ・ Reinhardt V. Metzger ・ Reinhardt van Rensburg ・ Reinhardt's fund ・ Reinhardt-Craig House, Kiln and Pottery Shop ・ Reinhardtia ・ Reinhardtsdorf Sandstone Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Reinhardt domain ： ウィキペディア英語版 Reinhardt domain In mathematics, especially several complex variables, an open subset $G$ of Cn is called Reinhardt domain if $(z\_1,\; \backslash dots,\; z\_n)\; \backslash in\; G$ implies $(e^\; z\_1,\; \backslash dots,\; e^\; z\_n)\; \backslash in\; G$ for all real numbers $\backslash theta\_1,\; \backslash dots,\; \backslash theta\_n$. 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 automorphism group has positive dimension: (1) $\backslash$ (polydisc); (2) $\backslash$ (unit ball); (3) (Thullen domain). In 1978, Toshikazu Sunada established a generalization of Thullen's result, and proved that two $n$-dimensional bounded Reinhardt domains $G\_1$ and $G\_2$ are mutually biholomorphic if and only if there exists a transformation $\backslash varphi:\backslash mathbf^n\backslash longrightarrow\; \backslash mathbf^n$ given by $z\_i\backslash mapsto\; r\_iz\_\; (r\_i>0)$, $\backslash sigma$ being a permutation of the indices), such that $\backslash varphi(G\_1)=G\_2$. == References == * * Lars Hörmander. ''An Introduction to Complex Analysis in Several Variables,'' North-Holland Publishing Company, New York, New York, 1973. * Peter Thullen, Zu den Abbildungen durch analytische Funktionen mehrerer komplexer Veraenderlichen Die Invarianz des Mittelpunktes von Kreiskoerpern, ''Matt. Ann.'' 104 (1931), 244-259 * Tosikazu Sunada, Holomorphic equivalence problem for bounded Reinhaldt domains, ''Math. Ann.'' 235 (1978), 111-128 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Reinhardt domain」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.