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Norme Minimale sur le Compléxifié d'un Espace de Hilbert Réel
http://hdl.handle.net/2261/1376
http://hdl.handle.net/2261/13764ef34777-faea-40ad-87ae-85e940a4320f
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
jms040102.pdf (186.5 kB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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| 公開日 | 2008-03-04 | |||||
| タイトル | ||||||
| タイトル | Norme Minimale sur le Compléxifié d'un Espace de Hilbert Réel | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源 | http://purl.org/coar/resource_type/c_6501 | |||||
| タイプ | departmental bulletin paper | |||||
| 著者 |
Avanissian, V.
× Avanissian, V. |
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| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | 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 % $$\align & \tilde\ell(z)\le\|z\|_{\Cal H_{\Bbb C}}\m\ \hbox{for}\m z\in\Cal H_{\Bbb C} \\ & \tilde\ell(x)=\|x\|_{\Cal H_{\Bbb R}}\m\ \hbox{for}\m x\in\Cal H_{\Bbb R}. \endalign$$ % 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 % $$\tilde D\supset D,\m\ \tilde D\cap\Bbb R^N=D\cap\Bbb R^N.$$ % 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 $\Bbb C^N$. |
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| 書誌情報 |
Journal of mathematical sciences, the University of Tokyo 巻 4, 号 1, p. 33-52, 発行日 1997 |
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| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 13405705 | |||||
| 書誌レコードID | ||||||
| 収録物識別子タイプ | NCID | |||||
| 収録物識別子 | AA11021653 | |||||
| フォーマット | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | application/pdf | |||||
| 日本十進分類法 | ||||||
| 主題Scheme | NDC | |||||
| 主題 | 415 | |||||
| Mathematical Reviews Number | ||||||
| MR1451302 | ||||||
| Mathmatical Subject Classification | ||||||
| 46C05(MSC1991) | ||||||
| Mathmatical Subject Classification | ||||||
| 31C10(MSC1991) | ||||||
| Mathmatical Subject Classification | ||||||
| 46A55(MSC1991) | ||||||
| Mathmatical Subject Classification | ||||||
| 52A40(MSC1991) | ||||||
| 出版者 | ||||||
| 出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
| 原稿受領日 | ||||||
| 1995-08-28 | ||||||
