HIRAI Takeshi 平井武

… Alternative Names

Researcher Number	70025310
Affiliation (based on the past Project Information) *help	2009 – 2010 : 京都大学, 名誉教授 2007 : 京都大学, 大学院・理学研究科, 名誉教授 1999 : 京都大学, 大学院理学研究科, 教授 1995 – 1999 : Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 1987 – 1994 : 京都大学, 理学部, 教授 1986 : Kyoto Univ. Fac. of Sci. Associate Professor, 理学部, 助教授
Review Section/Research Field	Principal Investigator 解析学 / Basic analysis Except Principal Investigator 解析学 / General mathematics (including Probability theory/Statistical mathematics) / 代数学・幾何学 / Algebra / Basic analysis
Keywords	Principal Investigator 表現論 / 調和解析 / 無限対称群 / function space / 作用素環 / 表現論と調和解析 / 量子情報理論 / 群のリ-ス積 / real analysis / 確率過程 … More Except Principal Investigator 表現論 / 双曲型方程式 / 解空間の構造 / 可解格子模型 / 確率微分方程式 / ユニタリ表現 / Harish-Chandra加群 / 量子群 / 半単純リー群 / 量子力学の方程式 / 力学系 / Brownian snake / Wiener汎関数 / 散乱理論 / 自由表面問題 / 保型表現 / Berezin変換 / 無限対称群 / Duffing方程式 / 流体方程式 / 離散系列 / 初期値問題 / スペクトル理論 / 調和解析 / べき零軌道 / 随伴多様体 / リー群 / ループ空間 / 確率解析 / 微分同相群 / 分岐問題 / 不変微分作用素 / 流体方程式系 / Equations in Quantum Mechanics / フラクタル / Fluid Dynamical Equations / 共形場理論 / 保型形式の空間 / 特異性の位数 / highest weight representation / Equation of Quantum Mechanics / 量子力学の方程式系 / Julia sets / singularity / Diffeomorphism Group / Periodic solutions of Duffing equations / 無限次元Hodge-Kodaira型作用素 / bifurcation problem in dynamical system / 周期 / Berezin Fransformation / 測度値分枝過程 / 流体の方程式 / 非線形偏微分方程式系 / リッチ曲率 / Borel de-Siebenthal離数系列 / conformal field theory / 量子力学的3体系 / 包絡環 / 関数解析学 / カオス / 複素力学系 / 最高ウェイト表現 / 漸近挙動 / 相函数 / Berezin 変換 / 代数曲面 / 指標 / ベクトル束 / Solvable lattice models / lattice spin system / 精度保証付き数値計算 / 環積 / ヘッケ作用素 / 力学系の分岐問題 / 解の特異性の伝播 / Dynamical System / 保型形式 / 準楕円性 / Sobolev空間 / 偏微分方程式 / 確率論 / 固有値問題 / Duffing方程式の周期解 / 非線形偏微分方程式 / ホイッタッカー模型 / Capelli Identity / 楕円型量子群 / Complex dynamics / multiplicity / Capelli等式 / Operator Theory / Structure of Solution Space / ウィナー汎関数 / Stochastic Diff.Eq. / Multiplicity-free Action / Hyperbolic P.D.E. / ウィナー汎関数のソボレフ空間 / Computer assisted proof / Wiener(ウィ-ナ-)汎関数 / 力学系理論 / Fourier integral operator / 一般Whittaker模型 / discrete series / Quasiconformal map / Equation of Fluid Dynamics / 対数ソボレフ不等式 / 正準変換 / リーマン面 / 旗多様体 / 計算機支援証明法 / Wiener空間上の解析学(Malliavin解析) / Stochastic Analysis / ホモクリニック倍分岐 / 超Wiener汎関数と一般化積分 / hyperbolic equation / Lie群 / Wiener空間上の解析学 / phase function / 冪零軌道 / エルミート対称空間 / Fractal sets / Bifurcation problems / 一階擬微分作用素 / トポロジ- / 対称群 / Dual Pair / Schrodinger operater / フ-リエ積分作用素 / Hecke operater / Fourier transform / Dirac 作用素 / 作用素論 / Nonlinear Part.Diff.Eq's / Lie superalgebra / 非線型解析 / measure valued branching processes / コンパクト化 / hypergroup / unitary representation / クライン群 / C^nの局所解析同型の芽の位相亜群 / 最高ウェイト加群 / Pauli作用素のスペクトル / innovation問題 / 超群 / 保型L函数 / Free Surface Problems / microlocal order / ラングラケポテンシャルを持つSchrodinger方程式 / 極小表現 / 量子確率論 / Riemann surface / 特異性 / Generalized Wiener functionals / 四元数型対称空間 / Harish-Chandara加群 / nilpotent orbit / Fractals / Sobolev spaces on Wiener space / 離散部分群 / eigenvalue problem / Bifurcation Th'y / Wiener Functional / 熱対流問題 / dual pair / リカッチ方程式 / generalized Whittaker model / 流体方程式の解空間の分岐 / Fluid dynamical equations / 力学系とカオス / Structure of solution space / シュレーディンガ作用素 / 指数定理 / 重複フリー作用 / 保証つき数値計算 / 無限次元リ-群の表現 / Whittaker模型 / アーベル多様体の周期 / Hausdorff dimension / Stochastic analysis / Validated Numerical Computation / 実調和解析 / Howe双対性 / innovation problem / タイヒミュラー空間 / 整関数力学系の変形理論 / 木村モデル / distribution / 基本解の構成 / 分岐理論 / 熱方程式の基本解の漸近理論 / ジュリア集合 / semisimple Lie群 / Quantum Group / 熱方程式の基本解 / Schrodinger方程式 / φ^4-格子場模型 / ヴェイユ表現 / ウィナー空間 / Wiener空間 / 双対性 / 代数学 / Kleinian groups / period of an abelian variety / モデュライ / differential operator of gradient type / bifurcations for equations in fluid dynamics / ヤンググラフ / Theory of Dynamical Systems / 超リー代数 / Euler-Maruyama近似 / Lie group / Harish-Chandra module / 表現の分岐 / カオス的アトラクター / 不変量 / 実効的双曲型 / フーリエ積分作用素 / 幾何学的Lorenzアトラクター / 熱核の近似スキーム / 双曲的変換 / 微分作用素環 / シュレディンガ-方程式 / Malliavrin解析 / Heisenberg群上の双曲型方程式 / Malliavin calculus / マルコフ半群の比較定理 / 表現の指標 / semisimple Lie group / 擬等角写像 / Spectral Theory / 幾何学的不変量 / 双曲的変換の離散部分群 / 計算機支援証明 / マリアヴァン解析 / 微分方程式系 / 熱方程式の基本解の漸近問題 / ジョルダン代数 / Lie Group / Dynamical Systems and Chaos / ハウスドルフ次元 / 超局所的位数 / 一般化Whittaker模型 / 重複度フリー作用 / 勾配型微分作用素 / フーリエ変換 / complex dynamics of entirefunctions / 重複度 / Asymptotic problems of heat kernels / Schrodinger型方程式 / 一段擬微分作用素 / 解析学 / 等方表現 / Quantum Group of Elliptic Type / 一般化されたWhittaker模型 / 周期解 / ユニタリ-表現 / ブラウン運動 / Whittakerベクトル / 分岐問題の計算機支援証明法 / Teichmuller space / グラスマン多様体 / フラクタル集合 / 離散系列表現 / 超函数 / Malliavin解析 / Jordan Algebra / canonical mapping / 逆問題 / 格子スピン系 / 条件付き測度 / Stochastic area / モジュラー形式 / Schrodinger作業素 / L-function / Capelli恒等式 / L函数 / 区間演算ソフトウェア- / テータ対応 Less

Integrated study of probability and representation theory towards harmonic analysis on huge groups
- Principal Investigator
  
  HORA Akihito
- Project Period (FY)
  2007 – 2010
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Basic analysis
- Research Institution
  Nagoya University
Modern study on homogeneous spaces and unitary representations via duality
- Principal Investigator
  
  YAMASHITA Hiroshi
- Project Period (FY)
  2006 – 2009
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  Basic analysis
- Research Institution
  Hokkaido University
無限次元調和解析Principal Investigator
- Principal Investigator
  
  平井武
- Project Period (FY)
  1998
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Kyoto University
Studies on the theory of representations of groups and algebrasPrincipal Investigator
- Principal Investigator
  
  HIRAI Takeshi
- Project Period (FY)
  1997 – 1998
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  解析学
- Research Institution
  KYOTO UNIVERSITY
Differential operators of gradient type on symmetric spaces and representations of Lie algebras
- Principal Investigator
  
  YAMASHITA Hiroshi
- Project Period (FY)
  1997 – 1999
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Algebra
- Research Institution
  Hokkaido University
実半単純リー群の表現とベき零軌道のケーリ-型変換
- Principal Investigator
  
  山下博
- Project Period (FY)
  1996
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Hokkaido University
Applied analysis of differential equations in math.sci.
- Principal Investigator
  
  NISHIDA Takaaki
- Project Period (FY)
  1996 – 1997
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  General mathematics (including Probability theory/Statistical mathematics)
- Research Institution
  KYOTO UNIVERSITY
Analysis and Applications of Teichmuller space
- Principal Investigator
  
  TANIGUCHI Masahiko
- Project Period (FY)
  1996
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  解析学
- Research Institution
  KYOTO UNIVERSITY
数理科学の微分方程式の解析的研究
- Principal Investigator
  
  西田孝明
- Project Period (FY)
  1995
- Research Category
  
  Grant-in-Aid for General Scientific Research (B)
- Research Field
  
  解析学
- Research Institution
  Kyoto University
Research on random phenomena by the methods of modern mathematics
- Principal Investigator
  
  WATANABE Shinzo
- Project Period (FY)
  1995 – 1998
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  General mathematics (including Probability theory/Statistical mathematics)
- Research Institution
  KYOTO UNIVERSITY
Research on automorphic representations
- Principal Investigator
  
  YOSHIDA Hiroyuki
- Project Period (FY)
  1994 – 1996
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  Algebra
- Research Institution
  KYOTO UNIVERSITY
Analytic and geometric studies of group representations and their applications
- Principal Investigator
  
  NOMURA Takaaki
- Project Period (FY)
  1994 – 1995
- Research Category
  
  Grant-in-Aid for General Scientific Research (B)
- Research Field
  
  解析学
- Research Institution
  KYOTO UNIVERSITY
確率過程論とloop空間上の確率解析
- Principal Investigator
  
  SHIGEKAWA Ichiro
- Project Period (FY)
  1993
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  General mathematics (including Probability theory/Statistical mathematics)
- Research Institution
  Kyoto University
Comprehensive study of real analysis and functional analysisPrincipal Investigator
- Principal Investigator
  
  HIRAI Takeshi
- Project Period (FY)
  1993 – 1994
- Research Category
  
  Grant-in-Aid for Co-operative Research (A)
- Research Field
  
  解析学
- Research Institution
  KYOTO UNIVERSITY
保型表現の研究
- Principal Investigator
  
  吉田敬之
- Project Period (FY)
  1992
- Research Category
  
  Grant-in-Aid for General Scientific Research (B)
- Research Field
  
  代数学・幾何学
- Research Institution
  Kyoto University
Modern Analysis for the Equations of Mathematical Science
- Principal Investigator
  
  NISHIDA Takaaki
- Project Period (FY)
  1992 – 1994
- Research Category
  
  Grant-in-Aid for General Scientific Research (A)
- Research Field
  
  解析学
- Research Institution
  KYOTO UNIVERSITY
C^∞ー写像の空間のトポロジ-
- Principal Investigator
  
  足立正久
- Project Period (FY)
  1991
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  Kyoto University
初期値問題の可解性と応用
- Principal Investigator
  
  IWASAKI N
- Project Period (FY)
  1991
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  解析学
- Research Institution
  Kyoto University
無限離散群の構造と表現の研究Principal Investigator
- Principal Investigator
  
  平井武
- Project Period (FY)
  1990
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  解析学
- Research Institution
  Kyoto University
Modern Mathematical Research for Equations in Mathematical Physics
- Principal Investigator
  
  NISHIDA Takaaki
- Project Period (FY)
  1990 – 1991
- Research Category
  
  Grant-in-Aid for General Scientific Research (B)
- Research Field
  
  解析学
- Research Institution
  Kyoto University
数理物理の現代数学的研究
- Principal Investigator
  
  IKEBE Teruo
- Project Period (FY)
  1989
- Research Category
  
  Grant-in-Aid for General Scientific Research (B)
- Research Field
  
  解析学
- Research Institution
  Kyoto University
ベクトル束の理論とその応用
- Principal Investigator
  
  丸山正樹
- Project Period (FY)
  1989
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  Kyoto University
無限次元群及び離散群のユニタリ表現の研究Principal Investigator
- Principal Investigator
  
  平井武
- Project Period (FY)
  1989
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  解析学
- Research Institution
  Kyoto University
Research on orders of singularities for solutions to partial differential equations
- Principal Investigator
  
  MIYATAKE Sadao
- Project Period (FY)
  1988 – 1989
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  解析学
- Research Institution
  Kyoto University, Faculty of Science
Lie superalgebraおよびLie群の表現の総合的研究Principal Investigator
- Principal Investigator
  
  平井武
- Project Period (FY)
  1987
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  解析学
- Research Institution
  Kyoto University
Mathematical Study on Stochastic Models
- Principal Investigator
  
  WATANABE Shinzo
- Project Period (FY)
  1987 – 1988
- Research Category
  
  Grant-in-Aid for General Scientific Research (B)
- Research Field
  
  General mathematics (including Probability theory/Statistical mathematics)
- Research Institution
  Kyoto University
Group-theoretical research of eigenvalue problems and its applications
- Principal Investigator
  
  YOSHIZAWA Hisaaki
- Project Period (FY)
  1985 – 1986
- Research Category
  
  Grant-in-Aid for General Scientific Research (B)
- Research Field
  
  General mathematics (including Probability theory/Statistical mathematics)
- Research Institution
  Kyoto University

All 2009 2008 2007

All Journal Article Presentation

[Journal Article] Towards projective representations and spin characters of finite and infinite complex reflection groups2009
- Author(s)
  T.Hirai, E.Hirai, A.Hora
- Journal Title
  
  Infinite Dimensional Harmonic Analysis Vol. 4
  
  Pages : 112-128
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19340032
[Journal Article] Limits of characters of wreath products Sn(T) of a compact group T with the symmetric groups and characters of S∞(T), I.2009
- Author(s)
  T. Hirai, E. Hirai, A. Hora
- Journal Title
  
  Nagoya Mathematical Journal 193
  
  Pages : 1-93
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19340032
[Journal Article] Limits of characters of wreath products Sn (T) of a compact group T with the symmetric groups and characters of S∞ (T), I.2009
- Author(s)
  T. Hirai, E. Hirai, A. Hora
- Journal Title
  
  Nagoya Mathematical Journal 193
  
  Pages : 1-93
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19340032
[Journal Article] Towards projective representations and spin characters of finite and infinite complex reflection groups2009
- Author(s)
  1T.Hirai, E.Hirai, A.Hora
- Journal Title
  
  Infinite Dimensional Harmonic Analysis Vol.4
  
  Pages : 122-128
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19340032
[Journal Article] Limits of characters of wreath products Sn(T) of a compact group T with the symmetric groups and characters of S∞(T),I.2009
- Author(s)
  T.Hirai, E.Hira, A.Hora
- Journal Title
  
  Nagoya Mathematical Journal Vol.193
  
  Pages : 1-93
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19340032
[Journal Article] Limits of characters of wreath products Sn(T) of a compact group T with the symmetric groups and characters of S∞(T), II. From a viewpoint of probability theory2008
- Author(s)
  A. Hora, T. Hirai, E. Hirai
- Journal Title
  
  Journal of Mathematical Society of Japan 60
  
  Pages : 1187-1217
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19340032
[Journal Article] Limits of characters of wreath products Sn (T) of a compact group T with the symmetric groups and characters of S∞ (T), II. From a viewpoint of probability theory2008
- Author(s)
  A. Hora, T. Hirai, E . Hirai
- Journal Title
  
  Journal of Mathematical Society of Japan 60
  
  Pages : 1187-1217
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19340032
[Journal Article] Limits of characters of wreath products Sn(T) of a compact group T with the symmetric groups and characters of S∞(T), II.2008
- Author(s)
  3A.Hora, T.Hirai, E.Hirai
- Journal Title
  
  From a viewpoint of probability theory, Journal of Mathematical Society of Japan Vol.60
  
  Pages : 1187-1217
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19340032
[Journal Article] Characters of wreath products of compact groups with the infinite symmetric group and characters of their canonical subgroups2007
- Author(s)
  T.Hirai, E.Hirai
- Journal Title
  
  Journal of Mathematics of Kyoto University Vol.47
  
  Pages : 269-320
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19340032
[Journal Article] Characters of wreath products of compact groups with the infinite symmetric group and characters of their canonical subgroups2007
- Author(s)
  T. Hirai, E. Hirai
- Journal Title
  
  J. Math. Kyoto Univ. 47
  
  Pages : 269-320
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19340032
[Presentation] 無限対称群および無限環積群の表現と指標2008
- Author(s)
  平井武
- Organizer
  日本数学会年会
- Place of Presentation
  近畿大学
- Year and Date
  2008-03-23
- Data Source
  KAKENHI-PROJECT-19340032

1. TANIGUCHI Masahiko (50108974)

# of Collaborated Projects : 11results

# of Collaborated Products : 0results
2. UMEDA Toru (00176728)

# of Collaborated Projects : 9results

# of Collaborated Products : 0results
3. WATANABE Shinzo (90025297)

# of Collaborated Projects : 8results

# of Collaborated Products : 0results
4. NOMURA Takaaki (30135511)

# of Collaborated Projects : 8results

# of Collaborated Products : 0results
5. IKEBE Teruo (00025280)

# of Collaborated Projects : 7results

# of Collaborated Products : 0results
6. NISHIDA Takaaki (70026110)

# of Collaborated Projects : 7results

# of Collaborated Products : 0results
7. YAMASHITA Hiroshi (30192793)

# of Collaborated Projects : 7results

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8. OHKAJI Takashi (20160426)

# of Collaborated Projects : 6results

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9. KOKUBU Hiroshi (50202057)

# of Collaborated Projects : 6results

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10. HIJIKATA Hiroaki (00025298)

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11. YOSHIDA Hiroyuki (40108973)

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12. 上野健爾 (40011655)

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13. 足立正久 (50025285)

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14. JIMBO Michio (80109082)

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15. YAMADA Hirofumi (40192794)

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16. SAITO Mutsumi (70215565)

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17. IWASAKI N (70027374)

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18. IWATSUKA Akira (40184890)

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19. IKEDA Tamotsu (20211716)

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20. SHIGEKAWA Ichiro (00127234)

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23. KUSUNOKI Yukio (90025221)

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24. HORA Akihito (10212200)

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25. SHIBUKAWA Youichi (90241299)

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26. KAWAZOE Takeshi (90152959)

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27. ISHI Hideyuki (00326068)

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28. 丸山正樹 (50025459)

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29. 西田吾郎 (00027377)

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30. YOSHIDA Tomoyuki (30002265)

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31. YAMAGUCHI Keizo (00113639)

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32. TACHIZAWA Kazuya (80227090)

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33. MATUMOTO Hisayosi (50272597)

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34. TANIGUCHI Kenji (20306492)

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35. WACHI Akihito (30337018)

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36. MATSUKI Toshihiko (20157283)

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37. SEKIGUCHI Jiro (30117717)

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38. SHIMENO Nobukazu (60254140)

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39. MORITA Hideaki (90435412)

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40. OKADA Soichi (20224016)

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41. TATE Tatsuya (00317299)

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42. OBATA Nobuaki (10169360)

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43. SHIMOMURA Hiroaki (20092827)

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44. ARAI Hitoshi (10175953)

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45. MATSUMOTO Sho (60547553)

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46. INAHAMA Yuzuru (80431998)

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47. KOMATSU Hikosaburo (40011473)

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48. TAKEMOTO Hideo (00004408)

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49. MINEMURA Katsuhiro (20060684)

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50. OHARU Shinnosuke (40063721)

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51. MIYACHI Akihiko (60107696)

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52. HIRAGA Kaoru (10260605)

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53. YOSHIDA Nobuo (40240303)

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54. TERAMOTO Yoshiaki (40237011)

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55. SUGAWA Toshiyuki (30235858)

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56. KIKUCHI Katsuhiko (50283586)

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57. YOSHIZAWA Hisaaki (50025219)

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58. YAMAGUTI Masaya (30025796)

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59. MIYATAKE Sadao (10025447)

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60. 戸田宏 (60025236)

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61. 竹井義次 (00212019)

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62. 本多尚文 (00238817)

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63. 斎藤公明 (90195983)

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64. 山口博 (20137798)

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65. 久保泉 (70022621)

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66. 河野明 (00093237)

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67. 吉野崇 (50005774)

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68. 藤原英徳 (50108643)

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69. 小谷眞一 (10025463)

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70. 松本和一郎 (40093314)

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HIRAI Takeshi 平井 武

平井 武 ヒライ タケシ

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無限次元調和解析Principal Investigator

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Studies on the theory of representations of groups and algebrasPrincipal Investigator

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Comprehensive study of real analysis and functional analysisPrincipal Investigator

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HIRAI Takeshi 平井武

平井武ヒライタケシ