{"created":"2024-12-19T00:53:21.456702+00:00","id":2002190,"links":{},"metadata":{"_buckets":{"deposit":"3b98e154-c62e-47e6-b31a-2bf94cf34750"},"_deposit":{"created_by":10,"id":"2002190","owner":"10","owners":[10],"pid":{"revision_id":0,"type":"depid","value":"2002190"},"status":"published"},"_oai":{"id":"oai:kansai-u.repo.nii.ac.jp:02002190","sets":["528:1588:1589:1591"]},"author_link":["54075","27719"],"control_number":"2002190","item_9_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2023-02-10","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"6","bibliographicPageEnd":"4171","bibliographicPageStart":"4145","bibliographicVolumeNumber":"376","bibliographic_titles":[{"bibliographic_title":"Transactions of the American Mathematical Society","bibliographic_titleLang":"en"}]}]},"item_9_description_4":{"attribute_name":"概要","attribute_value_mlt":[{"subitem_description":"Introducing the notion of extended Schrödinger spaces, we define the criticality and subcriticality of Schrödinger forms in the same manner as the recurrence and transience of Dirichlet forms, and give a sufficient condition for the subcriticality of Schrödinger forms in terms the bottom of spectrum. We define a subclass of Hardy potentials and prove that Schrödinger forms with potentials in this subclass are always critical, which leads us to optimal Hardy type inequality. We show that this definition of criticality and subcriticality is equivalent to that there exists an excessive function with respect to Schrödinger semigroup and its generating Dirichlet form through h-transform is recurrent and transient respectively. As an application, we can show the recurrence and transience of a family of Dirichlet forms by showing the criticality and subcriticaly of Schrödinger forms and show the other way around through h-transform, We give a such example with fractional Schrödinger operators with Hardy potential.","subitem_description_language":"en","subitem_description_type":"Other"}]},"item_9_description_5":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"The first author was supported in part by Grant-in-Aid for Scientific Research (No.18H01121(B)), Japan Society for the Promotion of Science. The second author was supported in part by Grant-in-Aid for Scientific Research (No.19K03552(C)), Japan Society for the Promotion of Science.","subitem_description_language":"en","subitem_description_type":"Other"}]},"item_9_publisher_34":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"American Mathematical Society","subitem_publisher_language":"en"}]},"item_9_relation_12":{"attribute_name":"DOI","attribute_value_mlt":[{"subitem_relation_type":"isVersionOf","subitem_relation_type_id":{"subitem_relation_type_id_text":"https://doi.org/10.1090/tran/8865","subitem_relation_type_select":"DOI"}}]},"item_9_rights_13":{"attribute_name":"権利","attribute_value_mlt":[{"subitem_rights":"© Copyright 2024 American Mathematical Society","subitem_rights_language":"en"}]},"item_9_source_id_10":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA00865686","subitem_source_identifier_type":"NCID"}]},"item_9_source_id_8":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"00029947","subitem_source_identifier_type":"PISSN"},{"subitem_source_identifier":"10886850","subitem_source_identifier_type":"EISSN"}]},"item_9_version_type_17":{"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_access_right":{"attribute_name":"アクセス権","attribute_value_mlt":[{"subitem_access_right":"open access","subitem_access_right_uri":"http://purl.org/coar/access_right/c_abf2"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Takeda, Masayoshi","creatorNameLang":"en"},{"creatorName":"竹田, 雅好","creatorNameLang":"ja"}],"familyNames":[{"familyName":"竹田","familyNameLang":"ja"},{"familyName":"Takeda","familyNameLang":"en"}],"givenNames":[{"givenName":"雅好","givenNameLang":"ja"},{"givenName":"Masayoshi","givenNameLang":"en"}],"nameIdentifiers":[{"nameIdentifier":"54075","nameIdentifierScheme":"WEKO"},{"nameIdentifier":"30179650","nameIdentifierScheme":"e-Rad_Researcher","nameIdentifierURI":"https://nrid.nii.ac.jp/ja/nrid/1000030179650"}]},{"creatorNames":[{"creatorName":"Uemura, Toshihiro","creatorNameLang":"en"},{"creatorName":"上村, 稔大","creatorNameLang":"ja"}],"familyNames":[{"familyName":"上村","familyNameLang":"ja"},{"familyName":"Uemura","familyNameLang":"en"}],"givenNames":[{"givenName":"稔大","givenNameLang":"ja"},{"givenName":"Toshihiro","givenNameLang":"en"}],"nameIdentifiers":[{"nameIdentifier":"27719","nameIdentifierScheme":"WEKO"},{"nameIdentifier":"30285332","nameIdentifierScheme":"e-Rad_Researcher","nameIdentifierURI":"https://nrid.nii.ac.jp/ja/nrid/1000030285332"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_access","date":[{"dateType":"Available","dateValue":"2024-12-19"}],"displaytype":"detail","filename":"KU-1100-20230210-01.pdf","filesize":[{"value":"306 KB"}],"format":"application/pdf","mimetype":"application/pdf","url":{"objectType":"fulltext","url":"https://kansai-u.repo.nii.ac.jp/record/2002190/files/KU-1100-20230210-01.pdf"},"version_id":"48b1116d-ea5c-4709-954d-2df4efaaef82"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"関西大学","subitem_subject_language":"ja","subitem_subject_scheme":"Other"},{"subitem_subject":"Kansai University","subitem_subject_language":"en","subitem_subject_scheme":"Other"}]},"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":"journal article","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"Criticality of Schrödinger forms and recurrence of Dirichlet forms","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Criticality of Schrödinger forms and recurrence of Dirichlet forms","subitem_title_language":"en"}]},"item_type_id":"9","owner":"10","path":["1591"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2024-12-19"},"publish_date":"2024-12-19","publish_status":"0","recid":"2002190","relation_version_is_last":true,"title":["Criticality of Schrödinger forms and recurrence of Dirichlet forms"],"weko_creator_id":"10","weko_shared_id":-1},"updated":"2024-12-19T02:26:50.525181+00:00"}