{"created":"2023-05-15T15:23:58.244531+00:00","id":10998,"links":{},"metadata":{"_buckets":{"deposit":"843ff5dd-7a0c-492e-afa6-a7bc1a61f818"},"_deposit":{"created_by":3,"id":"10998","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"10998"},"status":"published"},"_oai":{"id":"oai:sucra.repo.nii.ac.jp:00010998","sets":["84:296"]},"author_link":["16424"],"item_118_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"1998","bibliographicIssueDateType":"Issued"},"bibliographicVolumeNumber":"平成7-9年度","bibliographic_titles":[{"bibliographic_title":"科学研究費補助金(基盤研究 C)研究成果報告書"}]}]},"item_118_date_31":{"attribute_name":"作成日","attribute_value_mlt":[{"subitem_date_issued_datetime":"2009-01-15","subitem_date_issued_type":"Created"}]},"item_118_description_18":{"attribute_name":"識別番号 その他","attribute_value_mlt":[{"subitem_description":"KAKEN: 07640280","subitem_description_type":"Other"}]},"item_118_description_19":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"ホワイトノイズ解析における飛田微分に付随した新しいタイプのラプラシアンΔ_Pを無限次元多様体上に構成した。それは従来の飛田のラプラシアンΔ_Hとはことなり、C^∽不変性を有する良い性質の作用素として実現出来たため、ド・ラ-ム=ホッジ=小平の分解定理の無限次元版を示すことに成功した。\nホワイトノイズ解析における無限次元フ-リエ変換の変種として、擬FM変換Ψを構成し、基本的な諸性質を導出した。また特に IntertwiningPropertiesと呼ばれる性質やフォック展開表現など導いた。さらにその族{Ψ;_θ;∈R}が超汎関数空間(S)^*上の線形同相写像群の正則な1変数部分群を成し、しかもその対応する生成作用素がiN+iΔ^*_Gで与えられることが判明した。さらに、一般化FM変換 X_θを構成した。その族{Ψ_θ;∈R}はやはり(S)^*上の線形同相写像群の正則な1変数部分群であることを示した。また、その生成作用素の具体的表現を同定しその変換の特徴付け定理を証明した。\n確率変分方程式の解として、確率場X(s)がホワイトノイズ空間に実現され、そのS変換に対して古典的変分法が適用可という条件を課すと、特別な場合に限り変分操作が可能で、変分δXの具体的表現が得られた。\n確率境界値問題を考察し、ホワイトノイズ解析における手法を適用することにより、一般化された確率漸近解の定式化に基づき、確率解析的視点から解の構成を行った。また確率系の振動論の観点から、新しいタイプの極限定理を導いた。","subitem_description_type":"Abstract"}]},"item_118_description_20":{"attribute_name":"目次","attribute_value_mlt":[{"subitem_description":"1. Pseudo-Fourier-Mehler transform in white noise analysis and application of lifted convergence to a certain approximation Cauchy problem, Journal of Saitama University Mathematics and Natural Sciences II, 44-1 (1995),  p.55-79.\n2.ON PSEUDO-FOURIER-MEHLER TRANSFORMS AND INFINITESIMAL GENERATORS IN WHITE NOISE CALCULUS, ISAMU DOKU, 数理解析研究所講究録 RIMS Kokyuroku (Kyoto Univ.) 923 短期共同研究 ガウス空間上の作用素解析と量子確率論 (Analysis of Operators on Gaussian Space and Quantum Probability Theory) p.33-51\n3. Some Intertwining Properties of the Pseudo-Fourier-Mehler Transform\nJoumal of Saitama University Mathematics and Natural Sciences 45-1 (1995), p.1-9.\n4. A fock expansion of the Pseudo-Fourier-Mehler transform\nJournal of Saitama University Mathematics and Natural Sciences 45-1 (1995), p.11-16.\n5. On a class of infinite dimensional Fourier type transforms in white noise calculus, in Proceedings of the Seventh Japan-Russia Symposium on Probability Theory and Mathematical Statistics, JRPS95, Tokyo, july 26-30, 1995, (1996, World Scientific, Singapore), p.51-61.\n6. On the Laplacian on a space of white noise functionals, Tsukuba Joumal of Mathematics 19(1995), p.93-119.\n7. Tomonaga-Schwinger Supermany-Time Formalism and Hida's Stochastic Causal Calculus, Journal of Saitama University, Faculty of Education (Mathematics and Natural Science), Vol.44 No. 2 (1995), p.1-8\n8. Mathematical Aspects of Complex Canonical Quantization in Quantum Gravity, Journal of Saitama University, Faculty of Education (Mathematics and Natural Science). Vol.44 No. 2 (1995), p.9-19\n9. WHITE NOISE ANALYSIS AND THE BOUNDARY VALUE PROBLEM IN THE SPACE OF STOCHASTIC DISTRIBUTIONS, ISAMU DOKU, 数理解析研究所講究録 RIMS Kokyuroku (Kyoto Univ.) 957 量子確率解析とその周辺 (Quantum Stochastic Analysis and Related Fields) p.36-53","subitem_description_type":"Other"}]},"item_118_description_29":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"subitem_description":"text","subitem_description_type":"Other"}]},"item_118_description_30":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_118_text_3":{"attribute_name":"著者 ローマ字","attribute_value_mlt":[{"subitem_text_value":"Doku,  Isamu"}]},"item_118_text_32":{"attribute_name":"アイテムID","attribute_value_mlt":[{"subitem_text_value":"KK000446"}]},"item_118_text_4":{"attribute_name":"著者 所属","attribute_value_mlt":[{"subitem_text_value":"埼玉大学教育学部"}]},"item_118_text_5":{"attribute_name":"著者 所属(別言語)","attribute_value_mlt":[{"subitem_text_value":"Faculty of Education, Saitama University"}]},"item_118_text_9":{"attribute_name":"年月次","attribute_value_mlt":[{"subitem_text_value":"1998-3"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"道工, 勇"},{"creatorName":"ドウク, イサム","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2018-01-23"}],"displaytype":"detail","filename":"KK000446.pdf","filesize":[{"value":"7.3 MB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"KK000446.pdf","url":"https://sucra.repo.nii.ac.jp/record/10998/files/KK000446.pdf"},"version_id":"c813fd0e-4a75-453d-afa5-66b1ee5ab3c7"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"ホワイトノイズ解析","subitem_subject_scheme":"Other"},{"subitem_subject":"確率変分","subitem_subject_scheme":"Other"},{"subitem_subject":"無限次元解析学","subitem_subject_scheme":"Other"},{"subitem_subject":"ガウス系超汎関数","subitem_subject_scheme":"Other"},{"subitem_subject":"無限次元フ-リエ型変換","subitem_subject_scheme":"Other"},{"subitem_subject":"確率境界値問題","subitem_subject_scheme":"Other"}]},"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":"確率変分解析の基礎研究","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"確率変分解析の基礎研究"}]},"item_type_id":"118","owner":"3","path":["296"],"pubdate":{"attribute_name":"公開日","attribute_value":"2009-01-15"},"publish_date":"2009-01-15","publish_status":"0","recid":"10998","relation_version_is_last":true,"title":["確率変分解析の基礎研究"],"weko_creator_id":"3","weko_shared_id":3},"updated":"2023-05-15T19:10:16.766241+00:00"}