{"created":"2021-03-01T07:00:42.333803+00:00","id":41005,"links":{},"metadata":{"_buckets":{"deposit":"22d4b4fb-8feb-45c0-a9f0-238c9af0ccc2"},"_deposit":{"id":"41005","owners":[],"pid":{"revision_id":0,"type":"depid","value":"41005"},"status":"published"},"_oai":{"id":"oai:repository.dl.itc.u-tokyo.ac.jp:00041005","sets":["312:7290:7300","9:504:7292:7301"]},"item_4_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"1988","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"130","bibliographicPageStart":"69","bibliographicVolumeNumber":"38","bibliographic_titles":[{"bibliographic_title":"Scientific papers of the College of Arts and 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":"We consider an eigenvalue problem (1)-(2) : (1) $\\begin{pmatrix} 0 & 1 \\\\ 0 & 1 \\end{pmatrix} du(x)/dx +P(x)u(x)=\\lambda u(x)$ $(0\\leqq x\\leqq 1 ; u=\\begin{pmatrix} u_1 \\\\ u_2 \\end{pmatrix}$.  (2) $u_2()+hu_1(0)=0, u_2(1)+Hu_1(1)=0. $ Here $P=\\begin{pmatrix} a & b \\\\ (p_1) & (p_2) \\end{pmatrix} \\in {C^1[1,1]}^4 : $ : real-valued and h, H are real constants, and λ corresponds to an eigenvalue. We denote the set of eigenvalues of (1)-(2) by ${\\lambda _n)P,h,H)}_(n\\in Z)$ under an appropriate numbering. For $Q=\\begin{pmatrix} a & b \\\\ (q_1) & (q_2) \\end{pmatrix} \\in {C^1[0,1]}^4$ and $h, H, H^*, J, J^* \\in R\\setminus {-1,1} (H\\\neq H^*, J\\\neq J^*)$, we obtain the following result on continuous dependence of coefficients and boundary conditions upon eigenvalues : If $\\delta _0\\equiv \\sum _n^\\infty =_(-\\infty )(\\mid \\lambda _n(Q,h,J)-\\lambda _n(P,h,H)\\mid + (\\mid \\lambda _n(Q,h,J^*)-\\lambda _n(P,h,H^*)\\mid $ is sufficientrly small, then $\\parallel Q-P\\parallel _{[c^1[0,1]]^4}\\leqq +\\mid J-H\\mid +\\mid J^*-H^*\\mid \\leqq M\\delta _0$ for some constant M>0. Moreover we get $\\parallel Q-P\\parallel _{[c^1[0,1]]^4}\\leqq M$ . We show also that for given $\\mu _n, \\mu _n ^* \\in C (n\\in Z)$, there exists a unique $(Q,h,J^*)\\in {C^1[0,1]}^4 \\times (R\\setminus {-1,1})^2$ satisfying $\\lambda _n(Q, h, J)=\\mu _n$ and $\\mu _n(Q,h,j^*)=\\mu _n^*$ under appropriate assumptions on $\\mu _n, \\mu _n^*(n\\in Z)$ $(e.g. \\sum _n^\\infty =_(-\\infty )(\\mid \\mu _n - \\lambda _n(P,h,H^*)\\mid)$ is sufficiently small.). We prove these results by the principle of contraction mappings and, in order to apply the principle, we establish a priori estimates of solutions to some hyperbolic systems and results on perturbation of Riesz bases.","subitem_description_type":"Abstract"}]},"item_4_identifier_registration":{"attribute_name":"ID登録","attribute_value_mlt":[{"subitem_identifier_reg_text":"10.15083/00040996","subitem_identifier_reg_type":"JaLC"}]},"item_4_publisher_20":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"The University of Tokyo"}]},"item_4_source_id_10":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA10538733","subitem_source_identifier_type":"NCID"}]},"item_4_source_id_8":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"02897520","subitem_source_identifier_type":"ISSN"}]},"item_4_subject_15":{"attribute_name":"日本十進分類法","attribute_value_mlt":[{"subitem_subject":"410","subitem_subject_scheme":"NDC"}]},"item_4_text_4":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"Department of Mathematics, College of Arts and Sciences, University of Tokyo"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Yamamoto, Masahiro"}],"nameIdentifiers":[{"nameIdentifier":"139881","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":"scp038005.pdf","filesize":[{"value":"3.0 MB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"scp038005.pdf","url":"https://repository.dl.itc.u-tokyo.ac.jp/record/41005/files/scp038005.pdf"},"version_id":"ad4e0893-515d-4e64-92d2-64bce3c07453"}]},"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":"Continuous Dependence Problem in an Inverse Spectral Problem for Systems of Ordinary Differential Equations of First Order","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Continuous Dependence Problem in an Inverse Spectral Problem for Systems of Ordinary Differential Equations of First Order"}]},"item_type_id":"4","owner":"1","path":["7300","7301"],"pubdate":{"attribute_name":"公開日","attribute_value":"2008-11-19"},"publish_date":"2008-11-19","publish_status":"0","recid":"41005","relation_version_is_last":true,"title":["Continuous Dependence Problem in an Inverse Spectral Problem for Systems of Ordinary Differential Equations of First Order"],"weko_creator_id":"1","weko_shared_id":null},"updated":"2022-12-19T04:14:19.603761+00:00"}