{"created":"2023-07-27T06:52:31.618335+00:00","id":46503,"links":{},"metadata":{"_buckets":{"deposit":"8eb16303-2f35-4bea-8900-d436a40e4ee5"},"_deposit":{"created_by":18,"id":"46503","owners":[18],"pid":{"revision_id":0,"type":"depid","value":"46503"},"status":"published"},"_oai":{"id":"oai:kanazawa-u.repo.nii.ac.jp:00046503","sets":["2812:2813:2828"]},"author_link":["80533","2360"],"item_9_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2006-04","bibliographicIssueDateType":"Issued"},"bibliographicPageStart":"6p.","bibliographicVolumeNumber":"2003-2005","bibliographic_titles":[{"bibliographic_title":"平成17(2005)年度 科学研究費補助金 基盤研究(B) 研究成果報告書"},{"bibliographic_title":"2005 Fiscal Year Final Research Report","bibliographic_titleLang":"en"}]}]},"item_9_creator_33":{"attribute_name":"著者別表示","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Kasue, Atsushi"}],"nameIdentifiers":[{"nameIdentifier":"80533","nameIdentifierScheme":"WEKO"},{"nameIdentifier":"40152657","nameIdentifierScheme":"e-Rad","nameIdentifierURI":"https://kaken.nii.ac.jp/ja/search/?qm=40152657"}]}]},"item_9_description_21":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"リーマン多様体、リーマン多面体やサブリーマン多様体を特別に重要なクラスとして含む、保存的正則ディリクレ空間の族の収束とその極限の解析を行った。収束は、エネルギー形式に注目したガンマ収束およびスペクトル収束の意味である。以下主な成果内容を列記する。\n(1)スペクトル収束列の収束開集合列を取り上げ、核関数、グリーン関数、調和関数などの収束を示した。これによって、楕円型ハルナック不等式の成立しない状況においても、エネルギー最小解の列のエネルギーの集中によるある種の不連続性が極限空間の特異性に吸収されるという新しい知見も与えた。\n(2)距離グラフ(1次元リーマン多面体)あるいはネットワークの有効レジスタンスに注目して、収束理論を展開した。エネルギー形式に関するガンマ収束、距離構造に関するグロモフ-ハウスドルフ収束の関連を考察し、1次元特有の現象を収束理論の言葉で表現した。この収束の極限にはいわゆるフラクタル集合の代表的なクラスも含み、フラクタル集合上での解析の新しい視点を与えたことになる。\n(3)局所有限無限ネットワークは有限グラフの極限とも考えられ、その視点からロイデンのコンパクト化を考察した。ロイデンコンパクト化の擬等長不変性や、有効抵抗が一様に有界な場合においてはロイデンコンパクト化は距離づけ可能であることなどを証明するとともに、有界な幾何を持つ完備リーマン多様体の近似として双方の比較を行い、エネルギー有限な調和関数の空間の対応を明確にした。","subitem_description_type":"Abstract"},{"subitem_description":"We curried out the studies on convergence of conservative regular Dirichlet spaces and some analysis of the limit spaces. The set of spaces under consideration includes particularly Riemannian manifolds, Riemannian polyhedra, sub-Riemannian manifolds. The convergence is meant by a variational convergence, called the Gamma convergence, of energy forms and spectral convergence.\nThe main results are described as follows :\n(1)Considering a convergent sequence of open subsets of the spaces, we verified the convergence of the kernel functions, the Green functions, harmonic functions and so on. Moreover we showed a new insight into phenomena of concentration of energies of functions or more generally maps of least energy by describing it in terms of singularities of the limit spaces.\n(2)We developed the convergence theory concerning metric graphs, that is, one dimensional Riemannian polyhedra. In our arguments, the effective resistance plays important roles. Using this notion, we discussed the c onvergence of energy forms, the Dirichlet energy forms, in a certain variatinal sense, and also the metric structure of the graphs in the Gromov-Hausdorff sense. The theory features some particular phenomena on the set of one dimensional spaces. An important class of so called fractal sets is in fact included in our limit spaces. We proposed a new approach to the analysis on fractals.\n(3)Locally finite, infinite networks may be viewed as limits of finite networks. From this point of view, we studied Royden's compactification of infinite networks. Among other things, we proved the invariance of the Royden boundaries under quasi-isometric transformations, and further the metrizability of the Royden compactification under the condition of the effective resistance being bounded uniformly. Infinite networks can be considered as good approximations of complete Riemannian manifolds. We compared complete Riemannian manifolds with certain networks, focusing the functions of finite Dirichlet energies.","subitem_description_type":"Abstract"}]},"item_9_description_22":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"研究課題/領域番号:15340053, 研究期間(年度):2003-2007","subitem_description_type":"Other"},{"subitem_description":"出典：「測度距離空間の収束とエネルギー形式」研究成果報告書　課題番号15340053\n  (KAKEN：科学研究費助成事業データベース（国立情報学研究所）)\n　　　本文データは著者版報告書より作成","subitem_description_type":"Other"}]},"item_9_identifier_registration":{"attribute_name":"ID登録","attribute_value_mlt":[{"subitem_identifier_reg_text":"10.24517/00052835","subitem_identifier_reg_type":"JaLC"}]},"item_9_publisher_17":{"attribute_name":"公開者","attribute_value_mlt":[{"subitem_publisher":"金沢大学理工研究域数物科学系"}]},"item_9_relation_28":{"attribute_name":"関連URI","attribute_value_mlt":[{"subitem_relation_name":[{"subitem_relation_name_text":"https://kaken.nii.ac.jp/search/?qm=40152657"}],"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/search/?qm=40152657","subitem_relation_type_select":"URI"}},{"subitem_relation_name":[{"subitem_relation_name_text":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-15340053/"}],"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-15340053/","subitem_relation_type_select":"URI"}},{"subitem_relation_name":[{"subitem_relation_name_text":"https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-15340053/153400532005kenkyu_seika_hokoku_gaiyo/"}],"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-15340053/153400532005kenkyu_seika_hokoku_gaiyo/","subitem_relation_type_select":"URI"}}]},"item_9_version_type_25":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_ab4af688f83e57aa","subitem_version_type":"AM"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"加須栄, 篤"}],"nameIdentifiers":[{"nameIdentifier":"2360","nameIdentifierScheme":"WEKO"},{"nameIdentifier":"40152657","nameIdentifierScheme":"e-Rad","nameIdentifierURI":"https://kaken.nii.ac.jp/ja/search/?qm=40152657"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2018-11-19"}],"displaytype":"detail","filename":"SC-PR-KASUE-A-kaken 2006-6p.pdf","filesize":[{"value":"543.2 kB"}],"format":"application/pdf","licensetype":"license_11","mimetype":"application/pdf","url":{"label":"SC-PR-KASUE-A-kaken 2006-6p.pdf","url":"https://kanazawa-u.repo.nii.ac.jp/record/46503/files/SC-PR-KASUE-A-kaken 2006-6p.pdf"},"version_id":"57a384aa-f1a8-45a2-99c7-0751994cbafd"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"research report","resourceuri":"http://purl.org/coar/resource_type/c_18ws"}]},"item_title":"測度距離空間の収束とエネルギー形式","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"測度距離空間の収束とエネルギー形式"},{"subitem_title":"Convergence of metric measure spaces and energy forms","subitem_title_language":"en"}]},"item_type_id":"9","owner":"18","path":["2828"],"pubdate":{"attribute_name":"公開日","attribute_value":"2018-11-19"},"publish_date":"2018-11-19","publish_status":"0","recid":"46503","relation_version_is_last":true,"title":["測度距離空間の収束とエネルギー形式"],"weko_creator_id":"18","weko_shared_id":-1},"updated":"2024-07-01T06:20:15.638049+00:00"}