{"created":"2023-07-27T06:44:33.740053+00:00","id":34831,"links":{},"metadata":{"_buckets":{"deposit":"77e54d59-c8e3-4c27-9188-cb7a0d6c5282"},"_deposit":{"created_by":3,"id":"34831","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"34831"},"status":"published"},"_oai":{"id":"oai:kanazawa-u.repo.nii.ac.jp:00034831","sets":["2812:2813:2833"]},"author_link":["15115"],"item_9_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2001-03-01","bibliographicIssueDateType":"Issued"},"bibliographicPageStart":"14p.","bibliographicVolumeNumber":"1999-2000","bibliographic_titles":[{"bibliographic_title":"平成12(2000)年度 科学研究費補助金 基盤研究(B) 研究成果報告書"},{"bibliographic_title":"2000 Fiscal Year Final Research Report","bibliographic_titleLang":"en"}]}]},"item_9_creator_33":{"attribute_name":"著者別表示","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{}],"nameIdentifiers":[{},{},{}]}]},"item_9_description_21":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"本研究課題の最初の動機は、B.Helffer(1994-5)のカッツの転送作用素に関する仕事とRogava(1993)の作用素ノルムに関するリー・トロッター積公式に関する仕事であった.この2年間シュレーディンガー作用素論との関連に基づいてそれまでの研究を更に発展させ,上の2つの仕事を拡張する精緻な結果を得た.研究代表者・分担者の思想の根底には「スペクトル」という共通の水脈がある. 1.一瀬,高信敏はElectronic J.Prob.の論文で,確率解析的方法により,相対論的シュレーディンガー作用素を含む一般のレビ過程に付随した作用素に対応する転送作用素とシュレーディンガー半群との差のL^p作用素ノルム評価を小さい時間tのベキにより与えた.この成果は,非相対論的・相対論的シュレーディンガー作用素の両方の場合を統一的に扱った一瀬・高信の前論文(Nagoya Math.J.1998)の結果を含むばかりではなく,ある意味で,(磁場のある場合を除いた)すべての場合を包括するより一般のポテンシャルに対し,精密な結果を与えたものである. 2.一瀬,田村英男は,2つの非負自己共役作用素の作用素和が自己共役のときに,リー・トロッター・加藤積公式が作用素ノルムで収束することを証明した. 3.田村博志は,反例を構成することにより,我々の上の2の結果をサポートした. 4.田村英男は伊藤宏と共に,2次元磁場を持つ2次元シュレーディンガー作用素に対して,アハラノフ・ボーム効果を散乱振幅の漸近挙動によって見る興味ある研究も行った. 5.谷島賢二は,シュレーディンガー方程式の基本解の無限遠方でのふるまいが,ポテンシャル|x|^αのベキαが2より大きいか小さいかによって影響が如何に現れるかに関する興味深い研究を行った.","subitem_description_type":"Abstract"},{"subitem_description":"The research, primarily motivated by B.Helffer's work 1994-5 on the Kac transfer operator as well as Rogava's work in 1993 on the Lie-Trotter product formula in operator norm.\n(1) Ichinose and Takanobu considered the operator associated with the Levy process which is including the relativistic Schodinger operator, and proved (in Electronic J.Math.) by a probabilistic method based the Feynman-Kac formula sharp L^p-norm estimates between it semigroup and corresponding transfer operator.\n(2) Ichinose and Hideo Tamura has proved a very general result that the selfadjoint Lie-Trotter-Kato product formula holds in operator norm if the operator sum of two nonnegative selfadjoint operators is selfadjoint.\n(3) Hiroshi Tamura constructed an counterexample to support that our result in (2) is best possible.\n(4) Hideo Tamura keep studying with Hiroshi Ito the 2-demensional magnetic Schrodinger operator to watch the Aharanov-Bohm effect.\n(5) Yajima keeps studying how the fundamental solution of the Schrodinger equation behaves at infinity according as the potential is sub-quadratic or super-quadratic.","subitem_description_type":"Abstract"}]},"item_9_description_22":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"研究課題/領域番号:11440040, 研究期間(年度):1999–2000","subitem_description_type":"Other"},{"subitem_description":"出典：「カッツの転送作用素及びLie-Trotter積公式とその周辺の問題」研究成果報告書　課題番号11440040\n(KAKEN：科学研究費助成事業データベース（国立情報学研究所）)\n　　　本文データは著者版報告書より作成","subitem_description_type":"Other"}]},"item_9_publisher_17":{"attribute_name":"公開者","attribute_value_mlt":[{"subitem_publisher":"金沢大学理学部"}]},"item_9_relation_28":{"attribute_name":"関連URI","attribute_value_mlt":[{"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/search/?qm=20024044","subitem_relation_type_select":"URI"}},{"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11440040/","subitem_relation_type_select":"URI"}},{"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-11440040/114400402000kenkyu_seika_hokoku_gaiyo/","subitem_relation_type_select":"URI"}}]},"item_9_version_type_25":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_ab4af688f83e57aa","subitem_version_type":"AM"}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2017-10-05"}],"displaytype":"detail","filename":"SC-PR-KAMATA-K-kaken 2001-14p.pdf","filesize":[{"value":"750.0 kB"}],"format":"application/pdf","licensetype":"license_11","mimetype":"application/pdf","url":{"label":"SC-PR-KAMATA-K-kaken 2001-14p.pdf","url":"https://kanazawa-u.repo.nii.ac.jp/record/34831/files/SC-PR-KAMATA-K-kaken 2001-14p.pdf"},"version_id":"2a2685c3-38c8-41fb-8626-7cfad8f4c2c3"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"research report","resourceuri":"http://purl.org/coar/resource_type/c_18ws"}]},"item_title":"カッツの転送作用素及びLie-Trotter積公式とその周辺の問題","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"カッツの転送作用素及びLie-Trotter積公式とその周辺の問題"},{"subitem_title":"The Kac Transfer Operator, the Lie-Trotter Product Formula and Related Problems","subitem_title_language":"en"}]},"item_type_id":"9","owner":"3","path":["2833"],"pubdate":{"attribute_name":"公開日","attribute_value":"2017-10-05"},"publish_date":"2017-10-05","publish_status":"0","recid":"34831","relation_version_is_last":true,"title":["カッツの転送作用素及びLie-Trotter積公式とその周辺の問題"],"weko_creator_id":"3","weko_shared_id":3},"updated":"2023-07-27T14:46:07.525314+00:00"}