{"created":"2023-06-19T11:36:17.810232+00:00","id":3204,"links":{},"metadata":{"_buckets":{"deposit":"aac7a7af-f3ad-47bc-891d-793271900fcc"},"_deposit":{"created_by":13,"id":"3204","owners":[13],"pid":{"revision_id":0,"type":"depid","value":"3204"},"status":"published"},"_oai":{"id":"oai:mie-u.repo.nii.ac.jp:00003204","sets":["143:144:262:263"]},"author_link":["5334","5335"],"item_4_biblio_info_6":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2005-03-31","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"29","bibliographicPageStart":"1","bibliographicVolumeNumber":"56","bibliographic_titles":[{"bibliographic_title":"三重大学教育学部研究紀要. 自然科学・人文科学・社会科学・教育科学"}]}]},"item_4_description_14":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_4_description_4":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"三重大学の新田と名古屋大学の岡田によって汎関数空間上のFourier変換が定式化されたが、そこでの汎関数は\nƒ:{a:R→R}→Cというものを考えていた。一方、本論文ではdomainが測度空間（M, μ₀）の場合、すなわちƒ:{a:M→R}→Cの場合を考えた。そして汎関数空間上のFourier変換を行うために、新田・岡田の理論にしたがって2回の拡大を用いるが、新田・岡田の2回の拡大がどんな*Nの無限大数よりも大きいような☆（*N）の無限大数の存在を保証するために、特殊なフィルターを用いていたのに対し、ここでは自然数全体の集合上のフレシェ・フィルターを含む超フィルターを用いる一般的な2回の拡大で議論を行った。そしてその結果、新田・岡田の場合と同様の結果が得られた。また、本論文は3つの章から構成されており、第1章では超準解析の議論に必要な事を簡単に述べ、第2章では超準解析の応用として知られているローブ測度空間とルベーグ測度空間の対応について、結果のみ述べる。そして最後の第3章では、本論文の題名にもなっている一般の汎関数空間上のFourier変換、但しdomainが測度空間の場合について述べる。","subitem_description_type":"Abstract"}]},"item_4_publisher_30":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"三重大学教育学部"}]},"item_4_source_id_7":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"0389-9225","subitem_source_identifier_type":"PISSN"}]},"item_4_source_id_9":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA12097333","subitem_source_identifier_type":"NCID"}]},"item_4_text_18":{"attribute_name":"その他のタイトル","attribute_value_mlt":[{"subitem_text_language":"en","subitem_text_value":"Generalized Fourier Transformation for the Space of Functionals (Measure Space Domain)"}]},"item_4_text_65":{"attribute_name":"資源タイプ（三重大）","attribute_value_mlt":[{"subitem_text_value":"Departmental Bulletin Paper / 紀要論文"}]},"item_4_version_type_15":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_970fb48d4fbd8a85","subitem_version_type":"VoR"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"桑原, 克典","creatorNameLang":"ja"},{"creatorName":"Kuwahara, Katsunori","creatorNameLang":"en"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"新田, 貴士","creatorNameLang":"ja"},{"creatorName":"Nitta, Takashi","creatorNameLang":"en"}],"nameIdentifiers":[{}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2017-02-18"}],"displaytype":"detail","filename":"AA1209733305604.pdf","filesize":[{"value":"1.7 MB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"AA1209733305604.pdf","url":"https://mie-u.repo.nii.ac.jp/record/3204/files/AA1209733305604.pdf"},"version_id":"c6b7bb1f-2f72-46b8-858c-5f41ec39f1be"}]},"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":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"一般の汎関数空間上のFourier変換（domainが測度空間の場合）","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"一般の汎関数空間上のFourier変換（domainが測度空間の場合）","subitem_title_language":"ja"}]},"item_type_id":"4","owner":"13","path":["263"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2007-07-26"},"publish_date":"2007-07-26","publish_status":"0","recid":"3204","relation_version_is_last":true,"title":["一般の汎関数空間上のFourier変換（domainが測度空間の場合）"],"weko_creator_id":"13","weko_shared_id":-1},"updated":"2023-11-09T01:17:01.492749+00:00"}