{"created":"2023-07-27T06:44:31.866390+00:00","id":34788,"links":{},"metadata":{"_buckets":{"deposit":"78553867-ee92-46a4-b1f5-5df15052f479"},"_deposit":{"created_by":3,"id":"34788","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"34788"},"status":"published"},"_oai":{"id":"oai:kanazawa-u.repo.nii.ac.jp:00034788","sets":["2812:2813:2830"]},"author_link":["15115"],"item_9_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2004-03-01","bibliographicIssueDateType":"Issued"},"bibliographicPageStart":"16p.","bibliographicVolumeNumber":"2001-2003","bibliographic_titles":[{"bibliographic_title":"平成15(2003)年度科学研究費補助金 基盤研究(B) 研究成果報告書"},{"bibliographic_title":"2003 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":"Trotter-Kato積公式,または,Lie-Trotter-Kato積公式は,ふつうHilbert/Banach空間の強位相で収束するものであった.非自明なときに作用素ノルムでも成り立つ場合があることを知ったことが,本研究の動機であった. 1.一瀬は,田村英男との共著論文,及び田村英男,田村博志,海外研究協力者V.A.Zagrebnovとの2編の共著論文(Commun.Math.Phys.2001)において,2つの非負自己共役作用素の和が自己共役ならば作用素ノルム自己共役Trotter--Kato層公式が最良の誤差評価O(1/n)で成立することを確立した.この結果は,考えている状況で最良の最終的結果である.実際,以前に,一方では,Kacの転送作用素とSchroedinger半群の差のノルム評価を経たB.Helffer(1994-95)の最初の結果を拡張する一瀬・高信(Commun.Math.Phys.1997,Nagoya Math.J.1998,Electronic J.Prob.2000))によるFeynman-Kac-Ito公式を用いた確率解析的研究,百目鬼・一瀬・田村英男(J.Math.Soc.Japan 1998)及び一瀬・田村英男(symptotic Analysis 1998)による作用素論的研究の結果を,他方では,Rogava(1993)に始まる抽象的に作用素ノルム自己共役トロッター・加藤積公式を証明するそれまでの,山瀬・田村英男(Integral Equations Operator Theory 1997,Osaka J.Math.1998),Neidhardt-Zagrebnov(Integral Equations Operator Theory, Lett.Math.Phys.1998)等の研究結果をすべて陽に含み真に拡張するものである. 2.更に,一瀬は,H.Neidhardt及びV.A.Zagrebnovとの最近の共著論文(J.Functional Analysis 2004)において,1で確立した作用素ノルム自己共役トロッター・加藤積公式を作用素和の場合から2次形式和の場合へ,一方の自己共役作用素が他方の自己共役作用素によって2次形式の意味でドミネイトされるとき,これらの作用素の定義域に関するある付帯条件の下に拡張し,最良の誤差評価と共に証明した.このドミネイションを仮定しないで証明できるかどうかは今後の問題であろう.","subitem_description_type":"Abstract"},{"subitem_description":"The research is primarily motivated by B.Helffer's work 1994-5 on the Kac transfer operator as well as Rogava's work in 1993 on the selfadjoint Trotter-Kato product formula in operator norm.\n(1)Ichinose and Hideo Tamura proved a very general result to the effect that the selfadjoint Trotter-Kato product formula holds in operator norm if the operator sum of two nonnegative selfadjoint operators is selfadjoint, and also, with Hiroshi Tamura and V.A.Zagrebnov, this result with optimal error boundO(1/n).\n(2)Further, for the form sum case, Ichinose proved, with H.Neidhardt and V.A.Zagrebnov, the selfadjoint Trotter-Kato product formula in operator norm with optial error bound, in case where one of these operators is form-bounded with respect to the other, with some additional condition on the domains of these operators.\n(3)Hideo Tamura also studied with Hiroshi Ito the 2-dimensional magnetic Schrodinger operator to watch the Aharanov-Bohm effect through the asymptotic behaviour of the scattering amplitude.\n(4)Yajima studied local time-dcay of solutions of the time-periodic Schrodinger equation and the Nelson model in nonrelativistic quantum electrodynamics.","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:13440044, 研究期間(年度):2001–2003","subitem_description_type":"Other"},{"subitem_description":"出典：「作用素ノルムTrotter-Kato積公式の更なる展開と経路積分の問題」研究成果報告書　課題番号13440044\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-13440044/","subitem_relation_type_select":"URI"}},{"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-13440044/134400442003kenkyu_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 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Integral","subitem_title_language":"en"}]},"item_type_id":"9","owner":"3","path":["2830"],"pubdate":{"attribute_name":"公開日","attribute_value":"2017-10-05"},"publish_date":"2017-10-05","publish_status":"0","recid":"34788","relation_version_is_last":true,"title":["作用素ノルムTrotter-Kato積公式の更なる展開と経路積分の問題"],"weko_creator_id":"3","weko_shared_id":3},"updated":"2023-07-27T14:36:25.137713+00:00"}