{"created":"2023-06-20T16:41:08.298193+00:00","id":11554,"links":{},"metadata":{"_buckets":{"deposit":"5d51473c-5733-47ce-aea0-93ab8659778e"},"_deposit":{"created_by":3,"id":"11554","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"11554"},"status":"published"},"_oai":{"id":"oai:kindai.repo.nii.ac.jp:00011554","sets":["14:923:1809:1821","21:3039:3610:3618"]},"author_link":["22219","22218","22222","22220","22221"],"item_2_biblio_info_21":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2012-12-01","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"22","bibliographicPageStart":"17","bibliographicVolumeNumber":"17","bibliographic_titles":[{"bibliographic_title":"かやのもり：近畿大学産業理工学部研究報告"},{"bibliographic_title":"Reports of School of Humanity-Oriented Science and Engineering, Kinki University","bibliographic_titleLang":"en"}]}]},"item_2_description_33":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"[概要] 本論文は、月一回開催している学際セミナーのとくに、2012年度第14回、第15回セミナーで取り上げた「Elucidation and generalization of the Cooley-TUkey algorithm-CTA」において展開した、離散フーリエ変換の計算量を低減するアルゴリズムであるCTAを、群の表現を用いるダイアコーニス等の方法を用いて明らかにし、合わせて群とその表現(とくに群行列)の基礎を述べたものである。本セミナーの目的の一つである、大学教育における新たな教科書を作成する大いなる一歩であると確信している。本論文では、アーベル群の場合をのみを扱っているが、目標は、アウスランダー等の行った、冪零群の場合の非アーベル的フーリエ変換の計算量の低減を目標とする。ダイアコーニスの場合は、表現を付随させたベクトル値関数であり、ヴェンコフの場合のスペクトル理論の精神と類似しており、将来表現論的保型形式の研究にも通ずると信ずる。　　    [Abstract] In this paper, we shall elucidate the celebrated Cooley-Tukey (Cool and Tacky) algorithm [4] from representation-theoretic view point, following [6] in general and [1] in the case of nilpotent groups. We are concerned with non-Abelian Fourier transforms, which have many applications including one of the symmetric groups to statistics. Considering the Fourier transform with vector-valued function is rather efficient and can be studied together with Venkov's theory of automorphic forms with representations [17], [18], to be pursued subsequently. We shall also give some preliminaries on groups, linear representation of groups and group matrices.","subitem_description_type":"Abstract"}]},"item_2_description_41":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_2_publisher_14":{"attribute_name":"出版者 名前","attribute_value_mlt":[{"subitem_publisher":"近畿大学産業理工学部"}]},"item_2_source_id_22":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"13495801","subitem_source_identifier_type":"ISSN"}]},"item_2_text_8":{"attribute_name":"著者 所属","attribute_value_mlt":[{"subitem_text_value":"Kinki University"},{"subitem_text_value":"Kinki University"},{"subitem_text_value":"Kinki University"},{"subitem_text_value":"Kinki University"},{"subitem_text_value":"Kinki University"}]},"item_2_text_9":{"attribute_name":"著者所属(翻訳)","attribute_value_mlt":[{"subitem_text_value":"近畿大学産業理工学部情報学科; 講師"},{"subitem_text_value":"近畿大学産業理工学部電気通信工学科; 講師"},{"subitem_text_value":"近畿大学産業理工学部情報学科; 准教授"},{"subitem_text_value":"近畿大学産業理工学部情報学科; 教授"},{"subitem_text_value":"近畿大学産業理工学部電気通信工学科; 講師"}]},"item_2_version_type_12":{"attribute_name":"版","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":"TAKAHASHI,  K."}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"HIRANO,  G."}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"KAIDA,  T."}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"KANEMITSU,  S."}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"MATSUZAKI,  T."}],"nameIdentifiers":[{}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2016-02-19"}],"displaytype":"detail","filename":"AA12013209-20121225-0017.pdf","filesize":[{"value":"593.4 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"AA12013209-20121225-0017.pdf","url":"https://kindai.repo.nii.ac.jp/record/11554/files/AA12013209-20121225-0017.pdf"},"version_id":"cf847e8a-fa39-4210-8bcc-5c446b00b824"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"クーリータッキーアルゴリズム","subitem_subject_scheme":"Other"},{"subitem_subject":"有限フーリエ変換","subitem_subject_scheme":"Other"},{"subitem_subject":"表現論","subitem_subject_scheme":"Other"},{"subitem_subject":"計算量","subitem_subject_scheme":"Other"},{"subitem_subject":"Cooley-Tukey algorithm","subitem_subject_scheme":"Other"},{"subitem_subject":"CTA","subitem_subject_scheme":"Other"},{"subitem_subject":"Discrete Fourier Transforms","subitem_subject_scheme":"Other"},{"subitem_subject":"DFT","subitem_subject_scheme":"Other"},{"subitem_subject":"Representation Theory","subitem_subject_scheme":"Other"},{"subitem_subject":"Amount of computation","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"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":"〈Paper〉The Cool'n Tacky al-Khwarizmi","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"〈Paper〉The Cool'n Tacky al-Khwarizmi"}]},"item_type_id":"2","owner":"3","path":["1821","3618"],"pubdate":{"attribute_name":"公開日","attribute_value":"2013-02-04"},"publish_date":"2013-02-04","publish_status":"0","recid":"11554","relation_version_is_last":true,"title":["〈Paper〉The Cool'n Tacky al-Khwarizmi"],"weko_creator_id":"3","weko_shared_id":-1},"updated":"2023-06-20T23:30:52.863497+00:00"}