{"created":"2021-03-01T06:59:51.536994+00:00","id":40261,"links":{},"metadata":{"_buckets":{"deposit":"415b45d1-fe5a-4814-bbc1-1bfa82e9466b"},"_deposit":{"id":"40261","owners":[],"pid":{"revision_id":0,"type":"depid","value":"40261"},"status":"published"},"_oai":{"id":"oai:repository.dl.itc.u-tokyo.ac.jp:00040261","sets":["312:6865:7027:7035","9:504:6868:7029:7036"]},"item_4_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"1999","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"1","bibliographicPageEnd":"126","bibliographicPageStart":"101","bibliographicVolumeNumber":"6","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":"In the present paper we consider the number $\\cN_\\Om(\\la)$ of eigenvalues not exceeding $\\la$ of the negative Laplacian with homogeneous {\\sc Dirichlet} boundary conditions in a domain $\\Om\\subset\\RR^n$ with fractal boundary $\\partial \\Om$. It is known that for $\\la\\to\\infty$, $\\cN_\\Om(\\la)=\\cC_n|\\Om|_n\\la^{n/2}+O(\\la^{D/2})$, where $D$ is the {\\sc Minkowski} dimension of $\\partial\\Om$. For a certain class of domains with self--similar boundary, so-called \"\"fractal drums\"\", we obtain a second term of the form $-\\cF(\\ln\\la)\\,\\la^{D/2}$ with a bounded periodic function $\\cF$ and a third term. We investigate the function $\\cF$ which contains a generalized {\\sc Weierstrass} function with a self--similar fractal graph. Exact estimates for the {\\sc Minkowski} dimension for this graph will be presented.","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":"MR1683321"}]},"item_4_text_17":{"attribute_name":"Mathmatical Subject Classification","attribute_value_mlt":[{"subitem_text_value":"35P20(MSC1991)"}]},"item_4_text_33":{"attribute_name":"原稿受領日","attribute_value_mlt":[{"subitem_text_value":"1997-11-21"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Gerling, Jurgen"}],"nameIdentifiers":[{"nameIdentifier":"138858","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":"jms060106.pdf","filesize":[{"value":"256.5 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"jms060106.pdf","url":"https://repository.dl.itc.u-tokyo.ac.jp/record/40261/files/jms060106.pdf"},"version_id":"97ea53e7-9174-4953-be82-a33fe228235d"}]},"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":"Three-Term Asymptotics of the Spectrum of Self-Similar Fractal Drums","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Three-Term Asymptotics of the Spectrum of Self-Similar Fractal Drums"}]},"item_type_id":"4","owner":"1","path":["7035","7036"],"pubdate":{"attribute_name":"公開日","attribute_value":"2008-03-04"},"publish_date":"2008-03-04","publish_status":"0","recid":"40261","relation_version_is_last":true,"title":["Three-Term Asymptotics of the Spectrum of Self-Similar Fractal Drums"],"weko_creator_id":"1","weko_shared_id":null},"updated":"2022-12-19T04:15:32.692169+00:00"}