{"created":"2023-07-27T06:44:29.660113+00:00","id":34738,"links":{},"metadata":{"_buckets":{"deposit":"78082070-e453-45e1-8bfe-6e3972a0aea0"},"_deposit":{"created_by":3,"id":"34738","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"34738"},"status":"published"},"_oai":{"id":"oai:kanazawa-u.repo.nii.ac.jp:00034738","sets":["2812:2813:2827"]},"author_link":["39"],"item_9_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2007-05-01","bibliographicIssueDateType":"Issued"},"bibliographicPageStart":"7p.","bibliographicVolumeNumber":"2005-2006","bibliographic_titles":[{"bibliographic_title":"平成18(2006)年度 科学研究費補助金 基盤研究(C) 研究成果報告書"},{"bibliographic_title":"2006 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":"研究課題に関する当該研究期間(平成17年〜18年)における,主要な研究成果の概要は,以下の通りであり,学術雑誌等で発表された. 研究成果のひとつは,ハンケル変換に関する移植定理が実バーディ空間において成り立つことを証明したことである.移植定理とは,二つの直交関数系に対するそれぞれのフーリエ展開を考えた時,展開係数が同じであれば,それぞれのフーリエ展開が与える2つの関数のノルムが同値であることを主張する定理である.これは直交関数展開の調和解析における有効な道具である.ハンケル変換とは,その特殊な場合としてフーリエ変換を含む有用な積分変換である.実バーディ空間における作用素の評価は,補間によって,ルベーグ空間における対応する評価を導く.我々は,これら有用な枠組みにおいて,移植定理を得たものである. また,移植定理とは移植作用素の有界性を主張する定理と言える.この作用素は,ヒルベルト変換の一般化とも捕らえることが出来る.ヒルベルト変換は,ある条件を持つ関数を可積分関数に写すことが知られている.これをハンケル変換の移植作用素に対して示すことが出来た.さらに,この結果を用いてハンケル変換に関するチェザロ作用素の可積分関数の空間及び実バーディ空間における有界性を導くことが出来た. さらに,積分変換に関してバーディ空間で成り立つ古典的なペーリーの不等式に類似な不等式を得たことである.古典的なペーリーの不等式とは,実バーディ空間に属する関数のフーリエ級数展開を考えたとき,第n番目のフーリエ係数の絶対値の2乗をアダマールの間隙をもつnに渡って総和したものは収束し,その和は元の関数の実バーディ空間のノルムの2乗で押さえられると言うものである.我々は,この古典的なペーリーの不等式が,ハンケル変換に関して類似の形で成り立つことを示した.","subitem_description_type":"Abstract"},{"subitem_description":"Our main results of this research project are summarized as follows. The transplantation theorem for the Hankel transform has been proved on the real Hardy space. A transplantation operator is an operator which maps a function with the Fourier expansion in an orthogonal system to the function with the same Fourier coefficients with respect to another orthogonal system. A transplantation theorem is a theorem which asserts the boundedness of the transplantation operator. This type of theorem is a useful tool in harmonic analysis for orthogonal expansions. The Hankel transform is one of the integral transforms, and coincides with the Fourier transform as a special case. Estimations of operators on the real Hardy space allow us to get the corresponding estimations of the operators on the Lebesegue spaces. In such a useful scheme, we have obtained a transplantation theorem.\nTransplantation operators are regarded as a generalization of the Hilbert transform. It is known that the Hilbert transform maps a function with certain conditions to an integrable function. We have proved that the transplantation operators for the Hankel transform have the same properties. Using this result, we have showed that the Cesaro operators for the Hankel transform are bounded on the space of integrable functions and on the real Hardy space.\nWe have obtained Paley's inequality of integral transform type. The classical Paley inequality says that in the Fourier expansion of a function in the real Hardy space, the sum of the absolute values of its Fourier coefficients taken over the Hadamard gaps converges, and the sum is bounded by the square of the real Hardy space norm of the function. We have showed that an inequality of the same type as the classical Paley inequality holds for the Hankel transform.","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:17540155, 研究期間(年度):2005–2006","subitem_description_type":"Other"},{"subitem_description":"出典：「各種の直交関数展開に関連した調和解析の研究」研究成果報告書　課題番号17540155\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":"10.24517/00034725","subitem_identifier_reg_type":"JaLC"}]},"item_9_publisher_17":{"attribute_name":"公開者","attribute_value_mlt":[{"subitem_publisher":"金沢大学自然科学研究科"}]},"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-17540155/","subitem_relation_type_select":"URI"}},{"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-17540155/175401552006kenkyu_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 2007-7p.pdf","filesize":[{"value":"220.1 kB"}],"format":"application/pdf","licensetype":"license_11","mimetype":"application/pdf","url":{"label":"TE-PR-KANJIN-Y-kaken 2007-7p.pdf","url":"https://kanazawa-u.repo.nii.ac.jp/record/34738/files/TE-PR-KANJIN-Y-kaken 2007-7p.pdf"},"version_id":"9f2f9598-0a43-40cd-bfa1-ed9f2965eda7"}]},"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関連した調和解析の研究","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"各種の直交関数展開に関連した調和解析の研究"},{"subitem_title":"A study of harmonic analysis for orthogonal expansions","subitem_title_language":"en"}]},"item_type_id":"9","owner":"3","path":["2827"],"pubdate":{"attribute_name":"公開日","attribute_value":"2017-10-05"},"publish_date":"2017-10-05","publish_status":"0","recid":"34738","relation_version_is_last":true,"title":["各種の直交関数展開に関連した調和解析の研究"],"weko_creator_id":"3","weko_shared_id":3},"updated":"2023-07-27T14:34:58.195013+00:00"}