{"created":"2021-03-01T06:59:57.383581+00:00","id":40347,"links":{},"metadata":{"_buckets":{"deposit":"f6b99d53-9b2b-4bdc-88a8-6aa366a3b3c2"},"_deposit":{"id":"40347","owners":[],"pid":{"revision_id":0,"type":"depid","value":"40347"},"status":"published"},"_oai":{"id":"oai:repository.dl.itc.u-tokyo.ac.jp:00040347","sets":["312:6865:7063:7067","9:504:6868:7065:7068"]},"item_4_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"1995","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"2","bibliographicPageEnd":"346","bibliographicPageStart":"311","bibliographicVolumeNumber":"2","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 $H=-Δ+V(x)$ be the Schrodinger operator on ${\\bf R}^m$, $m\\ge 3$. We show that the wave operators $W_\\pm=\\lim_{t\\to\\pm\\infty}e^{itH}\\cdot e^{-itH_0}$, $H_0=-Δ$, are bounded in Sobolev spaces $W^{k, p}({\\bf R}^m)$, $1\\le p\\le\\infty$, $k=0, 1, \\ldots, \\ell$, if $V$ satisfies $\\|D^α V(y)\\|_{L^{p_0}(|x-y|\\le 1)}\\le C(1+|x|)^{-δ}$ for $δ>(3m/2)+1$, $p_0>m/2$ and $|α|\\le\\ell+\\ell_0$, where $\\ell_0=0$ if $m=3$ and $\\ell_0=[(m-1)/2]$ if $m\\ge 4$, $[σ]$ is the integral part of $σ$. This result generalizes the author's previous result which appears in J. Math.\\ Soc.\\ Japan 47, where the theorem is proved for the odd dimensional cases $m\\ge 3$ and several applications such as $L^p$-decay of solutions of the Cauchy problems for time-dependent Schrodinger equations and wave equations with potentials, and the $L^p$-boundedness of Fourier multiplier in generalized eigenfunction expansions are given.","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":"MR1366561"}]},"item_4_text_17":{"attribute_name":"Mathmatical Subject Classification","attribute_value_mlt":[{"subitem_text_value":"47A40(MSC1991)"},{"subitem_text_value":"35P25(MSC1991)"},{"subitem_text_value":"81Uxx(MSC1991)"}]},"item_4_text_33":{"attribute_name":"原稿受領日","attribute_value_mlt":[{"subitem_text_value":"1994-09-19"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Yajima, Kenji"}],"nameIdentifiers":[{"nameIdentifier":"138945","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":"jms020204.pdf","filesize":[{"value":"290.9 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"jms020204.pdf","url":"https://repository.dl.itc.u-tokyo.ac.jp/record/40347/files/jms020204.pdf"},"version_id":"e704581c-b5fc-4c95-8834-320378ddd034"}]},"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":"The $W^{k,p}$-continuity of wave operators for Schrödinger operators III, even dimensional cases $m\\geq4$","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"The $W^{k,p}$-continuity of wave operators for Schrödinger operators III, even dimensional cases $m\\geq4$"}]},"item_type_id":"4","owner":"1","path":["7067","7068"],"pubdate":{"attribute_name":"公開日","attribute_value":"2008-03-04"},"publish_date":"2008-03-04","publish_status":"0","recid":"40347","relation_version_is_last":true,"title":["The $W^{k,p}$-continuity of wave operators for Schrödinger operators III, even dimensional cases $m\\geq4$"],"weko_creator_id":"1","weko_shared_id":null},"updated":"2022-12-19T04:15:41.905141+00:00"}