{"_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"}, "item_4_biblio_info_7": {"attribute_name": "\u66f8\u8a8c\u60c5\u5831", "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": "\u30d5\u30a9\u30fc\u30de\u30c3\u30c8", "attribute_value_mlt": [{"subitem_description": "application/pdf", "subitem_description_type": "Other"}]}, "item_4_description_5": {"attribute_name": "\u6284\u9332", "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": "\u51fa\u7248\u8005", "attribute_value_mlt": [{"subitem_publisher": "Graduate School of Mathematical Sciences, The University of Tokyo"}]}, "item_4_source_id_10": {"attribute_name": "\u66f8\u8a8c\u30ec\u30b3\u30fc\u30c9ID", "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": "\u65e5\u672c\u5341\u9032\u5206\u985e\u6cd5", "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": "\u539f\u7a3f\u53d7\u9818\u65e5", "attribute_value_mlt": [{"subitem_text_value": "1997-11-21"}]}, "item_4_text_34": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7", "attribute_value_mlt": [{"subitem_text_value": "Departmental Bulletin Paper"}]}, "item_creator": {"attribute_name": "\u8457\u8005", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "Gerling, Jurgen"}], "nameIdentifiers": [{"nameIdentifier": "138858", "nameIdentifierScheme": "WEKO"}]}]}, "item_files": {"attribute_name": "\u30d5\u30a1\u30a4\u30eb\u60c5\u5831", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "2017-06-27"}], "displaytype": "detail", "download_preview_message": "", "file_order": 0, "filename": "jms060106.pdf", "filesize": [{"value": "256.5 kB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_free", "mimetype": "application/pdf", "size": 256500.0, "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": "\u8a00\u8a9e", "attribute_value_mlt": [{"subitem_language": "eng"}]}, "item_resource_type": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7", "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": "\u30bf\u30a4\u30c8\u30eb", "attribute_value_mlt": [{"subitem_title": "Three-Term Asymptotics of the Spectrum of Self-Similar Fractal Drums"}]}, "item_type_id": "4", "owner": "1", "path": ["312/6865/7027/7035", "9/504/6868/7029/7036"], "permalink_uri": "http://hdl.handle.net/2261/1247", "pubdate": {"attribute_name": "\u516c\u958b\u65e5", "attribute_value": "2008-03-04"}, "publish_date": "2008-03-04", "publish_status": "0", "recid": "40261", "relation": {}, "relation_version_is_last": true, "title": ["Three-Term Asymptotics of the Spectrum of Self-Similar Fractal Drums"], "weko_shared_id": null}