{"created":"2021-03-01T06:59:54.527912+00:00","id":40305,"links":{},"metadata":{"_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":["312:6865:7047:7053","9:504:6868:7049:7054"]},"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 % $$\\align & \\tilde\\ell(z)\\le\\|z\\|_{\\Cal H_{\\Bbb C}}\\m\\\n \\hbox{for}\\m z\\in\\Cal H_{\\Bbb C} \\\\ & \\tilde\\ell(x)=\\|x\\|_{\\Cal H_{\\Bbb R}}\\m\\\n \\hbox{for}\\m x\\in\\Cal H_{\\Bbb R}. \\endalign$$ % 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 $\\Bbb C^N$.","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_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","filename":"jms040102.pdf","filesize":[{"value":"186.5 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","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'un Espace de Hilbert Réel","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Norme Minimale sur le Compléxifié d'un Espace de Hilbert Réel"}]},"item_type_id":"4","owner":"1","path":["7053","7054"],"pubdate":{"attribute_name":"公開日","attribute_value":"2008-03-04"},"publish_date":"2008-03-04","publish_status":"0","recid":"40305","relation_version_is_last":true,"title":["Norme Minimale sur le Compléxifié d'un Espace de Hilbert Réel"],"weko_creator_id":"1","weko_shared_id":null},"updated":"2022-12-19T04:01:39.145582+00:00"}