WEKO3
アイテム
{"_buckets": {"deposit": "a154058b-8251-437f-a6a1-72ebad3d2127"}, "_deposit": {"id": "40305", "owners": [], "pid": {"revision_id": 0, "type": "depid", "value": "40305"}, "status": "published"}, "_oai": {"id": "oai:repository.dl.itc.u-tokyo.ac.jp:00040305", "sets": ["7053", "7054"]}, "item_4_biblio_info_7": {"attribute_name": "書誌情報", "attribute_value_mlt": [{"bibliographicIssueDates": {"bibliographicIssueDate": "1997", "bibliographicIssueDateType": "Issued"}, "bibliographicIssueNumber": "1", "bibliographicPageEnd": "52", "bibliographicPageStart": "33", "bibliographicVolumeNumber": "4", "bibliographic_titles": [{"bibliographic_title": "Journal of mathematical sciences, the University of Tokyo"}]}]}, "item_4_description_13": {"attribute_name": "フォーマット", "attribute_value_mlt": [{"subitem_description": "application/pdf", "subitem_description_type": "Other"}]}, "item_4_description_5": {"attribute_name": "抄録", "attribute_value_mlt": [{"subitem_description": "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 % $$\\align \u0026 \\tilde\\ell(z)\\le\\|z\\|_{\\Cal H_{\\Bbb C}}\\m\\\n \\hbox{for}\\m z\\in\\Cal H_{\\Bbb C} \\\\ \u0026 \\tilde\\ell(x)=\\|x\\|_{\\Cal H_{\\Bbb R}}\\m\\\n \\hbox{for}\\m x\\in\\Cal H_{\\Bbb R}. \\endalign$$ % 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 $\\Bbb C^N$.", "subitem_description_type": "Abstract"}]}, "item_4_publisher_20": {"attribute_name": "出版者", "attribute_value_mlt": [{"subitem_publisher": "Graduate School of Mathematical Sciences, The University of Tokyo"}]}, "item_4_source_id_10": {"attribute_name": "書誌レコードID", "attribute_value_mlt": [{"subitem_source_identifier": "AA11021653", "subitem_source_identifier_type": "NCID"}]}, "item_4_source_id_8": {"attribute_name": "ISSN", "attribute_value_mlt": [{"subitem_source_identifier": "13405705", "subitem_source_identifier_type": "ISSN"}]}, "item_4_subject_15": {"attribute_name": "日本十進分類法", "attribute_value_mlt": [{"subitem_subject": "415", "subitem_subject_scheme": "NDC"}]}, "item_4_text_16": {"attribute_name": "Mathematical Reviews Number", "attribute_value_mlt": [{"subitem_text_value": "MR1451302"}]}, "item_4_text_17": {"attribute_name": "Mathmatical Subject Classification", "attribute_value_mlt": [{"subitem_text_value": "46C05(MSC1991)"}, {"subitem_text_value": "31C10(MSC1991)"}, {"subitem_text_value": "46A55(MSC1991)"}, {"subitem_text_value": "52A40(MSC1991)"}]}, "item_4_text_33": {"attribute_name": "原稿受領日", "attribute_value_mlt": [{"subitem_text_value": "1995-08-28"}]}, "item_4_text_34": {"attribute_name": "資源タイプ", "attribute_value_mlt": [{"subitem_text_value": "Departmental Bulletin Paper"}]}, "item_creator": {"attribute_name": "著者", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "Avanissian, V."}], "nameIdentifiers": [{"nameIdentifier": "138902", "nameIdentifierScheme": "WEKO"}]}]}, "item_files": {"attribute_name": "ファイル情報", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "2017-06-27"}], "displaytype": "detail", "download_preview_message": "", "file_order": 0, "filename": "jms040102.pdf", "filesize": [{"value": "186.5 kB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_free", "mimetype": "application/pdf", "size": 186500.0, "url": {"label": "jms040102.pdf", "url": "https://repository.dl.itc.u-tokyo.ac.jp/record/40305/files/jms040102.pdf"}, "version_id": "093bee08-ef97-41c7-b3aa-daccb3628a2a"}]}, "item_language": {"attribute_name": "言語", "attribute_value_mlt": [{"subitem_language": "eng"}]}, "item_resource_type": {"attribute_name": "資源タイプ", "attribute_value_mlt": [{"resourcetype": "departmental bulletin paper", "resourceuri": "http://purl.org/coar/resource_type/c_6501"}]}, "item_title": "Norme Minimale sur le Compléxifié d\u0027un Espace de Hilbert Réel", "item_titles": {"attribute_name": "タイトル", "attribute_value_mlt": [{"subitem_title": "Norme Minimale sur le Compléxifié d\u0027un Espace de Hilbert Réel"}]}, "item_type_id": "4", "owner": "1", "path": ["7053", "7054"], "permalink_uri": "http://hdl.handle.net/2261/1376", "pubdate": {"attribute_name": "公開日", "attribute_value": "2008-03-04"}, "publish_date": "2008-03-04", "publish_status": "0", "recid": "40305", "relation": {}, "relation_version_is_last": true, "title": ["Norme Minimale sur le Compléxifié d\u0027un Espace de Hilbert Réel"], "weko_shared_id": null}
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)
|
|
Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
---|---|---|---|---|---|---|
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. |
|||||
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 $\Bbb C^N$. |
|||||
書誌情報 |
Journal of mathematical sciences, the University of Tokyo 巻 4, 号 1, p. 33-52, 発行日 1997 |
|||||
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 | 415 | |||||
主題Scheme | NDC | |||||
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 |