{"created":"2021-03-01T06:20:42.558617+00:00","id":4054,"links":{},"metadata":{"_buckets":{"deposit":"94d15035-efb0-4de1-b71a-fd378b9567d0"},"_deposit":{"id":"4054","owners":[],"pid":{"revision_id":0,"type":"depid","value":"4054"},"status":"published"},"_oai":{"id":"oai:repository.dl.itc.u-tokyo.ac.jp:00004054","sets":["312:391","9:233:280"]},"item_7_alternative_title_1":{"attribute_name":"その他のタイトル","attribute_value_mlt":[{"subitem_alternative_title":"シュレディンガー方程式に対する分散型及びストリッカーツ評価"}]},"item_7_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2011-03-24","bibliographicIssueDateType":"Issued"},"bibliographic_titles":[{}]}]},"item_7_date_granted_25":{"attribute_name":"学位授与年月日","attribute_value_mlt":[{"subitem_dategranted":"2011-03-24"}]},"item_7_degree_grantor_23":{"attribute_name":"学位授与機関","attribute_value_mlt":[{"subitem_degreegrantor":[{"subitem_degreegrantor_name":"University of Tokyo (東京大学)"}]}]},"item_7_degree_name_20":{"attribute_name":"学位名","attribute_value_mlt":[{"subitem_degreename":"博士(数理科学)"}]},"item_7_description_5":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"The present paper is concerned with LP -smoothing properties of solutions to time dependentSchriidinger equations. Vve study two kinds of V-smoothing properties, namely theStrichar:f;z estimates and the dispersive estimates.The first part is concerned with Strichartz estimates for Schriidinger equations onscattering manifolds which are non-compact manifolds with asymptotically conic ends.It is shown that time-local Strichartz estimates, outside a large compact set centered atorigin, hold for any admissible pair (including the endpoint). Moreover, we prove globalin space Strichartz estimates under the nontrapping condition of the geodesic flow. \\¥ealso study a relationship between Strichartz estimates and microlocal properties of thesolution. More precisely, it is shown that (local in time) Strichartz estimates follow fromthe dispersive estimates for spatial and frequency localized solutions. This part is basedon a paper \" Strichartz estimates for Schriidinger equations on scattering manifolds \" .The second part is concerned with dispersive estimates for scattering solutions toone-dimensional Schriidinger equations with potentials. We prove a weighted dispersiveestimate for the non-resonant state with stronger time decay than the case of the usualunweighted estimate. Furthermore asymptotic expansions in time of scattering solutionsare given. This part is based on a paper \"Dispersive estimates and asymptotic expansionsfor Schriidinger equations in dimension one\" to appear in Journal of the MathematicalSociety ofJapan.","subitem_description_type":"Abstract"}]},"item_7_dissertation_number_26":{"attribute_name":"学位授与番号","attribute_value_mlt":[{"subitem_dissertationnumber":"甲第27194号"}]},"item_7_full_name_3":{"attribute_name":"著者別名","attribute_value_mlt":[{"nameIdentifiers":[{"nameIdentifier":"9353","nameIdentifierScheme":"WEKO"}],"names":[{"name":"水谷, 治哉"}]}]},"item_7_identifier_registration":{"attribute_name":"ID登録","attribute_value_mlt":[{"subitem_identifier_reg_text":"10.15083/00004045","subitem_identifier_reg_type":"JaLC"}]},"item_7_select_21":{"attribute_name":"学位","attribute_value_mlt":[{"subitem_select_item":"doctoral"}]},"item_7_subject_13":{"attribute_name":"日本十進分類法","attribute_value_mlt":[{"subitem_subject":"410","subitem_subject_scheme":"NDC"}]},"item_7_text_22":{"attribute_name":"学位分野","attribute_value_mlt":[{"subitem_text_value":"Mathematical Sciences (数理科学)"}]},"item_7_text_24":{"attribute_name":"研究科・専攻","attribute_value_mlt":[{"subitem_text_value":"Graduate School of Mathematical Sciences (数理科学研究科)"}]},"item_7_text_27":{"attribute_name":"学位記番号","attribute_value_mlt":[{"subitem_text_value":"博数理第375号"}]},"item_7_text_4":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"東京大学大学院数理科学研究科"},{"subitem_text_value":"Graduate School of Mathematical Sciences, The University of Tokyo"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"MIzutani, Haruya"}],"nameIdentifiers":[{"nameIdentifier":"9352","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":"2017-06-01"}],"displaytype":"detail","filename":"MIzutaniH_23_3_PhD_a.pdf","filesize":[{"value":"2.5 MB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"MIzutaniH_23_3_PhD_a.pdf","url":"https://repository.dl.itc.u-tokyo.ac.jp/record/4054/files/MIzutaniH_23_3_PhD_a.pdf"},"version_id":"661edbf0-1481-4ceb-ada7-f84c9567de04"},{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2017-06-01"}],"displaytype":"detail","filename":"MIzutaniH_23_3_PhD_b.pdf","filesize":[{"value":"71.2 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"MIzutaniH_23_3_PhD_b.pdf","url":"https://repository.dl.itc.u-tokyo.ac.jp/record/4054/files/MIzutaniH_23_3_PhD_b.pdf"},"version_id":"8d952b87-e191-46ac-8482-9802ce82a03d"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"Strichartz estimate","subitem_subject_scheme":"Other"},{"subitem_subject":"Dispersive estimate","subitem_subject_scheme":"Other"},{"subitem_subject":"Asymptotic expansion","subitem_subject_scheme":"Other"},{"subitem_subject":"Schriidinger equation","subitem_subject_scheme":"Other"},{"subitem_subject":"Scattering manifold.","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":"thesis","resourceuri":"http://purl.org/coar/resource_type/c_46ec"}]},"item_title":"Dispersive and Strichartz estimates for Schrodinger equations","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Dispersive and Strichartz estimates for Schrodinger equations"}]},"item_type_id":"7","owner":"1","path":["391","280"],"pubdate":{"attribute_name":"公開日","attribute_value":"2012-10-23"},"publish_date":"2012-10-23","publish_status":"0","recid":"4054","relation_version_is_last":true,"title":["Dispersive and Strichartz estimates for Schrodinger equations"],"weko_creator_id":"1","weko_shared_id":null},"updated":"2022-12-19T03:45:49.014362+00:00"}