UTokyo Repository 東京大学
 

UTokyo Repository >
121 数理科学研究科 >
Journal of Mathematical Sciences, the University of Tokyo >

このページ(論文)をリンクする場合は次のURLを使用してください: http://hdl.handle.net/2261/1376

タイトル: Norme Minimale sur le Compléxifié d'un Espace de Hilbert Réel
著者: Avanissian, V.
発行日: 1997年
出版者: Graduate School of Mathematical Sciences, The University of Tokyo
掲載誌情報: Journal of Mathematical Sciences, The University of Tokyo. Vol. 4 (1997), No. 1, Page 33-52
抄録: Let $\Cal H_{\Bbb R}$ be a real Hilbert space and let $\Cal H_{\Bbb C}$ be the complexification of $\Cal H_{\Bbb R}$. The first part of this paper treats the problem of the existence of the minimal norm $\tilde\ell$ on $\Cal H_{\Bbb C}$ such that % $$\align & \tilde\ell(z)\le\|z\|_{\Cal H_{\Bbb C}}\m\n \hbox{for}\m z\in\Cal H_{\Bbb C} \\ & \tilde\ell(x)=\|x\|_{\Cal H_{\Bbb R}}\m\n \hbox{for}\m x\in\Cal H_{\Bbb R}. \endalign$$ % We prove the following theorem : a)\m The minimal norme $\tilde\ell$ exists in $\Cal H_{\Bbb C}$. b)\m Let $D\subset\Bbb C^N$ be a bounded, convex, balanced domain. There exists a maximal bounded convex, balanced domain $\tilde D\subset\Bbb C^N$ such that % $$\tilde D\supset D,\m\n \tilde D\cap\Bbb R^N=D\cap\Bbb R^N.$$ % c)\m Let $\Cal H_{\Bbb C}=\Bbb C^N$, then the minimal norm $\tilde\ell$ is the supporting function of the unit closed Lie ball in $\Bbb C^N$. (a) and b) extend a result of K. T. Hahn and Peter Plug) where $\Cal H_{\Bbb R}=\Bbb R^N$ and $D$ is the unit euclidean ball in $\Cal C^N$. The second part of the paper gives a geometrical interpretation of the minimal norm $\tilde\ell$ in $\Cal H_{\Bbb C}$. If $\Cal N$ is a norm in $\Bbb C^N$, log $\Cal N(z)$ is plurisubharmonic function. The final part of the paper studies the plurisubharmonic functions $V$ in $\Bbb C^N$ such that $\forall k\in\Bbb C$, $V(kz)=|k|V(z)$, $V(z)\le\|z\|$ for $z\in\Bbb C^N$, $V(x)=\|x\|$ for $x\in\Bbb R^N$, $\|z\|$ is euclidean norm in $\Bbb C^N$.
URI: http://hdl.handle.net/2261/1376
ISSN: 13405705
出現カテゴリ:Journal of Mathematical Sciences, the University of Tokyo
Journal of Mathematical Sciences, the University of Tokyo

この論文のファイル:

ファイル 記述 サイズフォーマット
jms040102.pdf182.15 kBAdobe PDF見る/開く

本リポジトリに保管されているアイテムはすべて著作権により保護されています。

 

Valid XHTML 1.0! DSpace Software Copyright © 2002-2010  Duraspace - ご意見をお寄せください