{"created":"2023-07-27T06:44:33.110768+00:00","id":34816,"links":{},"metadata":{"_buckets":{"deposit":"bd9ca42d-e1ee-4bf3-84e4-dbdf24a9c79d"},"_deposit":{"created_by":3,"id":"34816","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"34816"},"status":"published"},"_oai":{"id":"oai:kanazawa-u.repo.nii.ac.jp:00034816","sets":["2812:2813:2831"]},"author_link":["39"],"item_9_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2003-04-01","bibliographicIssueDateType":"Issued"},"bibliographicPageStart":"5p.","bibliographicVolumeNumber":"2001-2002","bibliographic_titles":[{"bibliographic_title":"平成14(2002)年度 科学研究費補助金 基盤研究(C) 研究成果報告書"},{"bibliographic_title":"2002 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":[{}],"nameIdentifiers":[{},{},{}]}]},"item_9_description_21":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"当該研究課題に関する研究実績の概要は次の通りであり,成果は学術雑誌等に発表された. 研究代表者堪甚は,解析関数の作る古典的なハーディー空間に対して成り立つ,いわゆるペーリーの不等式を,ヤコビ多項式の作る直交系に対して証明した.証明の鍵は,近時調和解析において得られた,実ハーディー空間の双対空間がBMO空間となると言う定理である.この定理によって,これまで複素解析的手法によって証明されていた定理が実解析的手法で解析出来るようになった.我々は,この考えを直交関数系の調和解析に有効と見て取り前述の定理を得た.上述の双対定理は,言い換えると実ハーディー空間のアトム分解である.このアトム分解を使って,古典的なハーディー空間に対して成り立つもうひとつの不等式,ハーディーの不等式をヤコビ多項式の作る直交関数系へと一般化した.更に代表者は,チェザロ作用素,一般にハウスドルフ作用素を研究した.そして,ある種の条件の下でハウスドルフ作用素が,1より小さい指数を持つ実ハーディー空間上で,有界な作用素となることを示した. また,研究分担者は各々の立場から以下の成果を得た.土谷は拡散過程のディリクレ形式の収束性を,基礎となる測度を固定せずに論じた.一瀬は,作用素ノルムでの自己共役トロッター・加藤積公式に関して,以前に得ていた結果に,更に新しい結果を加えた.また,極座標表示のディラック方程式の基本解を構成し経路積分の問題を考察した.佐藤は,積分核に単位球面上でLlog L条件を仮定すると,これにより定義されるマルチンキービィッツ関数がweak(1,1)評価を満足することを示した.藤解は,特殊ワイエルシュトラス・ピー関数に係数を持つリッカチ微分方程式を研究し,その解が有理型である事を示した.","subitem_description_type":"Abstract"},{"subitem_description":"Our research results are summarized as follows. The head investigator Kanjin has obtained Paley's inequality and Hardy's inequality with respect to the Jacobi expansions. The classical Peley's inequality and Hardy's inequality are two of the most familiar inequalities on the Fourier coefficients of functions in the Hardy space of certain analytic functions in the unit disc. The inequalities were originally proved by complex method. It is difficult to study orthogonal expansions by using complex method. Recent development of the real Hardy space theory, especially the atomic decomposition characterization or the real Hardy space and BMO space duality, allows to discuss problems on inequalities with respect to orthogonal expansions. Our Hardy's inequality have proved by applying the atomic decomposition to the Jacobi function system and Our Paley's inequality has gotten by using the real Hardy space and BMO space duality. Further, he has studied the Cesaro operator and, generally, the Hausdorff operator. The result says that the Hausdorff operator is bounded on the real Hardy space with parameter p smaller than one under some conditions.\nThe investigator Tsuchiya has investigated convergence of Dirichlet forms of diffusion process without assuming that the underlying measures are fixed or compatible with a fixed one. Ichinose has obtained more results on the self-adjoint Trotter-Kate product formula with operator norm. Sato has considered Marcinkiewicz integrals arising from rough kernels satisfying LlogL condition on the unit (n-l)-sphere and proved the weak type (1,1) estimates. Tohge has studied a Riccati differential equation whose coefficient is expressible in terms of a special Weierstrass pe-function and shown that all the solutions are meromorphic.","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:13640160, 研究期間(年度):2001–2002","subitem_description_type":"Other"},{"subitem_description":"出典：「各種の直交関数展開にかかわる調和解析」研究成果報告書　課題番号13640160\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":"10.24517/00034803","subitem_identifier_reg_type":"JaLC"}]},"item_9_publisher_17":{"attribute_name":"公開者","attribute_value_mlt":[{"subitem_publisher":"金沢大学工学部"}]},"item_9_relation_28":{"attribute_name":"関連URI","attribute_value_mlt":[{"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/search/?qm=50091674","subitem_relation_type_select":"URI"}},{"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640160/","subitem_relation_type_select":"URI"}},{"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-13640160/136401602002kenkyu_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_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2017-10-05"}],"displaytype":"detail","filename":"TE-PR-KANJIN-Y-kaken 2003-5p.pdf","filesize":[{"value":"116.3 kB"}],"format":"application/pdf","licensetype":"license_11","mimetype":"application/pdf","url":{"label":"TE-PR-KANJIN-Y-kaken 2003-5p.pdf","url":"https://kanazawa-u.repo.nii.ac.jp/record/34816/files/TE-PR-KANJIN-Y-kaken 2003-5p.pdf"},"version_id":"006a5eba-4e81-4bb0-9d98-bbedaf5c54d8"}]},"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":"各種の直交関数展開にかかわる調和解析","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"各種の直交関数展開にかかわる調和解析"},{"subitem_title":"Harmonic Analysis for Some Orthogonal Expansions","subitem_title_language":"en"}]},"item_type_id":"9","owner":"3","path":["2831"],"pubdate":{"attribute_name":"公開日","attribute_value":"2017-10-05"},"publish_date":"2017-10-05","publish_status":"0","recid":"34816","relation_version_is_last":true,"title":["各種の直交関数展開にかかわる調和解析"],"weko_creator_id":"3","weko_shared_id":3},"updated":"2023-07-27T14:41:23.255054+00:00"}