TAKAGI Hiroyuki 高木啓行

… Alternative Names

高木啓行タカギヒロユキ

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Researcher Number	20206725
Other IDs
External Links
Affiliation (based on the past Project Information) *help	2014 – 2017: 信州大学, 学術研究院理学系, 教授 2015 – 2016: 信州大学, 理学部, 教授 2010 – 2013: 信州大学, 理学部, 教授 2006 – 2008: 信州大学, 理学部, 教授 2001 – 2003: 信州大学, 理学部, 講師 1995 – 1996: 信州大学, 理学部, 講師 1993 – 1994: 信州大学, 理学部, 助手
Review Section/Research Field	Principal Investigator Basic analysis / 解析学 Except Principal Investigator 解析学 / Basic analysis / General mathematics (including Probability theory/Statistical mathematics) / Algebra / Geometry / Basic analysis / Geometry
Keywords	Principal Investigator 合成作用素 / 保存問題 / バナッハ環 / シフト作用素 / 関数解析学 / 荷重合成作用素 / 乗法作用素 / Fredholm作用素 / コンパクト作用素 / Hardy空間 … More / 関数環 / スペクトル / 等長作用素 / Bloch空間 / Zygmund空間 / Hermitian operator … More Except Principal Investigator 不変部分空間 / 非線形問題 / 関数方程式論 / 爆発・非爆発問題 / 大域解析学 / ハーディ空間 / 不変環 / ブルゲイン代数 / ハ-ディ族 / バーグマン族 / 等距離線型写像 / ブルガン環 / 無限分解可能過程 / 無限分解可能確率場 / 安定確率場 / 確率場の同等問題 / 確率場の積分表現 / 球関数 / エルミート形式 / ヘッケ環 / 同時固有関数 / 局所密度 / 球等質空間 / Todaの積 / Whitehead積 / Jamesホモトピー切除定理 / Hoof空間 / 対称空間 / (DO-P)形式 / BKW作用素 / 異方的フラクタル / バナッハ環 / C*環 / 等距離写像 / 代数構造 / ユニタリー群 / 正値可逆元 / Thmpson距離 / 有界解析関数空間 / 閉イデアル / 極大イデアル空間 / 特異内部関数 / 合成作用素 / ブラシュケ積 / グリースン部分 / 有界解析関数環 / 合成作甲素 / 国際研究者交流 / アメリカ:中国 / アメリカ : アルゼンチン : 中国 / 外部関数 / 等長作用素 / Space of analytic functions / closed ideal / maximal ideal space / singular inner function / composition operator / invariant subspace / Blaschke product / Gleason Pant / Banach algebra / Segal algebra / Fourier algebra / Lau algebra / quasi-topology / Hyers-Ulam stability / inequality / topological semigroup / BSE and BED / multipliers / fractional operation / inversion map / distributive law / Archimedean semigroup / fixed point theorem / Ulam type stability / linear isometry / Jensen type inequality / Archimedean group / differential equation / Jensen's inequality / 関数空間 / 荷重合成作用素 / 線形作用素 / リーマン多様体 / 射影極限の力学系 / 等長変換 / 一般射影極限 / 無限次元 / カオス Less

荷重合成作用素の保存構造の研究Principal Investigator
- Principal Investigator
  
  高木啓行
- Project Period (FY)
  2015 – 2017
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Shinshu University
Geometric-topological study on dynamics of infinite dimensional linear operators
- Principal Investigator
  
  KAWAMURA Kazuhiro
- Project Period (FY)
  2014 – 2016
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  University of Tsukuba
Classifications of commutative Banach algebras and Banach modules and its applications
- Principal Investigator
  
  TAKAHASI Sin-ei
- Project Period (FY)
  2013 – 2015
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Toho University
Studies on structures and isometries of commutative Banach algebrasPrincipal Investigator
- Principal Investigator
  
  TAKAGI Hiroyuki
- Project Period (FY)
  2011 – 2014
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Shinshu University
Study on preserver problems on Banach alebras
- Principal Investigator
  
  HATORI Osamu
- Project Period (FY)
  2010 – 2012
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Niigata University
Studies on composition operators and spectrum-preserving mapsPrincipal Investigator
- Principal Investigator
  
  TAKAGI Hiroyuki
- Project Period (FY)
  2006 – 2008
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Shinshu University
Structure of ideals in the space of bounded analytic functions and operator theory
- Principal Investigator
  
  IZUCHI Keiji
- Project Period (FY)
  2001 – 2003
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Basic analysis
- Research Institution
  NIIGATA UNIVERSITY
対称空間上の球関数
- Principal Investigator
  
  広中由美子
- Project Period (FY)
  1996
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Shinshu University
ホモトピー論に関わる空間構造の研究
- Principal Investigator
  
  向井純夫
- Project Period (FY)
  1996
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Shinshu University
無限分解可能過程をめぐる諸問題
- Principal Investigator
  
  井上和行
- Project Period (FY)
  1995
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  General mathematics (including Probability theory/Statistical mathematics)
- Research Institution
  Shinshu University
Bergman族とHardy族
- Principal Investigator
  
  真次康夫
- Project Period (FY)
  1994
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  解析学
- Research Institution
  Shinshu University
非線形問題に関する数理力学的総合研究
- Principal Investigator
  
  板谷信敏
- Project Period (FY)
  1993
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  解析学
- Research Institution
  Shinshu University
関数空間上の荷重合成作用素についてPrincipal Investigator
- Principal Investigator
  
  高木啓行
- Project Period (FY)
  1993
- Research Category
  
  Grant-in-Aid for Encouragement of Young Scientists (A)
- Research Field
  
  解析学
- Research Institution
  Shinshu University

All 2018 2017 2016 2015 2014 2013 2011 2009 2008 2007 2006 Other

All Journal Article Presentation Book

[Book] フーリエ解析入門(プリンストン解析学講義I)2007
- Author(s)
  エリアス・M・スタイン, ラミ・シャカルチ著, 新井仁之, 杉本充, 高木啓行, 千原浩之訳
- Total Pages
  312
- Publisher
  日本評論社
- Data Source
  KAKENHI-PROJECT-18540167
[Book] 『翻訳書』スタイン&シャカルチ「フーリエ解析入門」(プリンストン解析講義)2007
- Author(s)
  新井仁之・杉本充・高木啓行・千原浩之(訳者)
- Publisher
  日本評論社
- Data Source
  KAKENHI-PROJECT-18540167
[Journal Article] Peculiar homomorphisms on algebras of vector valued maps2018
- Author(s)
  Osamu Hatori, Shiho Oi and Hiroyuki Takagi
- Journal Title
  
  Studia Mathematica
  
  Volume: 242 Issue: 2 Pages: 141-163
- DOI
  10.4064/sm8799-6-2017
- Description
  Publish online
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15K04897, KAKENHI-PROJECT-17K05241, KAKENHI-PROJECT-15K04921, KAKENHI-PROJECT-16K05172
[Journal Article] Peculiar homomorphisms on algebras of vector-valued continuously differentiable maps2017
- Author(s)
  Osamu Hatori, Shiho Oi and Hiroyuki Takagi
- Journal Title
  
  Linear and Nonlinear Analysis
  
  Volume: 3 Pages: 101-109
- Peer Reviewed / Acknowledgement Compliant / Open Access
- Data Source
  KAKENHI-PROJECT-15K04897
[Journal Article] A characterization of multipliers of a Lau algebra constructed by semisimple commutative Banach algebras2016
- Author(s)
  Sin-Ei Takahasi, Hiroyuki Takagi and Takeshi Miura
- Journal Title
  
  Taiwanese Journal of Mathematics
  
  Volume: 20 Issue: 6 Pages: 1401-1415
- DOI
  10.11650/tjm.20.2016.7386
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-26400080, KAKENHI-PROJECT-15K04897, KAKENHI-PROJECT-15K04921, KAKENHI-PROJECT-16K05172
[Journal Article] Ulam type stability problems for alternative homomorphisms2014
- Author(s)
  S-E. Takahasi, M. Tsukada, T. Miura, H. Takagi and K. Tanahashi
- Journal Title
  
  J. Inequal. Appl.
  
  Volume: 2014 Issue: 1 Pages: 1-13
- DOI
  10.1186/1029-242x-2014-228
- NAID
  120007101195
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-23540193, KAKENHI-PROJECT-25400120
[Journal Article] Ulam type stability problems for alternative homomorphisms2014
- Author(s)
  S.Takahashi, M. Tsukada, T. Miura, H. Takagi and K.Tanahasi
- Journal Title
  
  Journal of Inequalities and applications
  
  Volume: 228 Pages: 1-13
- NAID
  120007101195
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-26400080
[Journal Article] Real-linear isometries between subspaces of continuous functions2014
- Author(s)
  H. Koshimizu, T. Miura, H. Takagi and S.-E. Takahasi
- Journal Title
  
  J. Math. Anal. Appl.
  
  Volume: 413 Issue: 1 Pages: 229-241
- DOI
  10.1016/j.jmaa.2013.11.050
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-23740097, KAKENHI-PROJECT-25400120, KAKENHI-PROJECT-26400080
[Journal Article] Real-linear isometries between subspaces of continuous functions2014
- Author(s)
  H. Koshimizu, T. Miura, H. Takagi and S.-E. Takahasi
- Journal Title
  
  J. Math. Anal. Appl.
  
  Volume: 413 Pages: 229-241
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540193
[Journal Article] Backward shifts on function algebras2011
- Author(s)
  Hiroyuki Takagi, Hironao Koshimizu andHiroaki Ariizumi
- Journal Title
  
  J. Math. Anal. Appl
  
  Volume: vol.377 Pages: 135-144
- NAID
  120007114269
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540178
[Journal Article] Backward shifts on function algebras2011
- Author(s)
  Hiroyuki Takagi
- Journal Title
  
  Jour.Math.Anal.Appl.
  
  Volume: 377 Pages: 135-144
- NAID
  120007114269
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540178
[Journal Article] Spectral radii conditions for isomorphisms between unital semisimple commutative Banach algebras2011
- Author(s)
  G. Hirasawa, T. Miura and H. Takagi
- Journal Title
  
  Contemp. Math.
  
  Volume: 547 Pages: 125-134
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540193
[Journal Article] Backward shifts on function algebras2011
- Author(s)
  H. Takagi, H. Koshimizu and H. Ariizumi
- Journal Title
  
  J. Math. Anal. Appl.
  
  Volume: 377 Pages: 135-144
- NAID
  120007114269
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540193
[Journal Article] A Cauchy-Euler type factorization of operators2008
- Author(s)
  S.-E. Takahasi, H. Oka, T. Miura, H. Takagi
- Journal Title
  
  Tokyo J. Math 31
  
  Pages: 489-493
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540167
[Journal Article] A generalization of Wang's inequality2007
- Author(s)
  T. Miura, H. Takagi, S.-E. Takahasi
- Journal Title
  
  Applied Functional Analysis, Yokohama Publ.
  
  Pages: 203-210
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540167
[Journal Article] Unital and multiplicatively spectrumpreserving surjections between semisimple commutative Banach algebras are linear and multiplicative2007
- Author(s)
  O.Hatori, T. Miura and H. Takagi
- Journal Title
  
  J.Math. Anal. 326
  
  Pages: 281-296
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540167
[Journal Article] 2-local isometries and 2-local automorphisms on uniform algebras2007
- Author(s)
  O. Hatori, T. Miura, H. Oka and H. Takagi
- Journal Title
  
  Int. Math Forum 2
  
  Pages: 2491-2502
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540167
[Journal Article] Exponential type functional equation andits Hyers-Ulam stability2007
- Author(s)
  S.-E. Takahasi, T. Miura, H. Takagi
- Journal Title
  
  J. Math. Anal 329
  
  Pages: 1191-1203
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540167
[Journal Article] Unital and multiplicatively spectrum-preserving surjections between semi-simple commutative Banach algebras are linear and multiplicative2007
- Author(s)
  Osamu Hatori, Takeshi Miura, Hiroyuki Takagi
- Journal Title
  
  Journal of Mathematical Analysis and Applications 326
  
  Pages: 281-296
- Data Source
  KAKENHI-PROJECT-18540167
[Journal Article] Exponential type functional equation and its Hyers-Ulam stability2007
- Author(s)
  Sin-Ei Takahasi, Takeshi Miura, Hiroyuki Takagi
- Journal Title
  
  Journal of Mathematical Analysis and Applications 329
  
  Pages: 1191-1203
- Data Source
  KAKENHI-PROJECT-18540167
[Journal Article] Continuously differentiable means2006
- Author(s)
  J.-I. Fujii, M. Fujii, T. Miura, H. Takagi and S.-E, Takahasi
- Journal Title
  
  J.Inequal. Appl.
  
  Pages: 15-15
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540167
[Journal Article] Characterizations of isometric isomorphisms between uniform algebras via nonlinear range-preserving properties2006
- Author(s)
  Osamu Hatori, Takeshi Miura, Hiroyuki Takagi
- Journal Title
  
  Proceeding of the American Mathematical Society 134
  
  Pages: 2923-2930
- Data Source
  KAKENHI-PROJECT-18540167
[Journal Article] Characterizations of isometric isomorphisms between uniform algebras via nonlinear range-preserving properties2006
- Author(s)
  O.Hatori, T. Miura and H. Takagi
- Journal Title
  
  Proc.Amer.Math 134
  
  Pages: 2923-2930
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540167
[Journal Article] A reconsideration of Hua's inequality II2006
- Author(s)
  J.-I. Fujii, M. Fujii, T. Miura, H. Takagi and S.-E. Takahasi
- Journal Title
  
  J.Inequal. Appl.
  
  Pages: 8-8
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540167
[Journal Article] Superstability of generalized multiplicative functionals
- Author(s)
  T. Miura, H. Takagi, M. Tsukada and S.-E. Takahasi
- Journal Title
  
  to appear in J. Inequal. Appl.
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540167
[Journal Article] Peripheral multiplicativitiy of maps on uniformly closed algebras of continuous functions which vanish at infinity
- Author(s)
  O. Hatori, T. Miura, H. Oka and H. Takagi
- Journal Title
  
  to appear in Tokyo J. Math.
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540167
[Presentation] Banach空間上のシフト作用素の存在性について2018
- Author(s)
  古清水大直, 高木啓行
- Organizer
  第5回山陰基礎論・解析学研究集会
- Place of Presentation
  皆生の宿ゆるり 1F会議室竹仙(鳥取県・米子市)
- Year and Date
  2018-01-07
- Data Source
  KAKENHI-PROJECT-15K04897
[Presentation] リプシッツ環の間のコンパクトな準同型写像2017
- Author(s)
  高木啓行
- Organizer
  2016年度つくばセミナー
- Place of Presentation
  筑波大学
- Year and Date
  2017-03-06
- Data Source
  KAKENHI-PROJECT-15K04897
[Presentation] Ⅰ型半単純可換Banach環の分類について2017
- Author(s)
  高橋眞映、三浦毅、井上純治、高木啓行
- Organizer
  日本数学会年会（函数解析学分科会）
- Place of Presentation
  首都大学
- Year and Date
  2017-03-25
- Data Source
  KAKENHI-PROJECT-15K04897
[Presentation] Banach空間上の等長作用素の形について2017
- Author(s)
  古清水大直, 高木啓行
- Organizer
  平成29年度名古屋若手セミナー
- Place of Presentation
  岐阜大学教育学部(岐阜県・岐阜市)
- Year and Date
  2017-12-27
- Data Source
  KAKENHI-PROJECT-15K04897
[Presentation] A Lau algebra of type I defined by semi-simple commutative Banach algebras2016
- Author(s)
  Sin-Ei Takahasi, Hiroyuki Takagi and Takeshi Miura
- Organizer
  RIMS研究集会 Research on isometires from various view points
- Place of Presentation
  京都大学数理解析研究所（京都府京都市左京区）
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-26400080
[Presentation] Peculiar homomorphisms on commutative Banach algebras of vector-valued functions2016
- Author(s)
  Osamu Hatori, Shiho Oi and Hiroyuki Takagi
- Organizer
  RIMS研究集会　Research on isometries from various view points
- Place of Presentation
  京都大学数理解析研究所（京都府京都市左京区）
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-26400080
[Presentation] Peculiar homomorphisms on commutative Banach algebras of vector-valued functions2016
- Author(s)
  Osamu Hatori, Shiho Oi and Hiroyuki Takagi
- Organizer
  RIMS work shop : Researches on isometries form various viewpoints
- Place of Presentation
  京都大学数理研
- Year and Date
  2016-11-02
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K04897
[Presentation] A Lau algebra of type I defined by semisimple commutative algebras2016
- Author(s)
  Sin-Ei Takahasi, Takeshi Miura and Hiroyuki Takagi
- Organizer
  RIMS work shop : Researches on isometries from various viewpoints
- Place of Presentation
  京都大学数理研
- Year and Date
  2016-11-01
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K04897
[Presentation] 有界正則関数のなすバナッハ環の間の等距離写像2016
- Author(s)
  高木啓行
- Organizer
  つくばセミナー
- Place of Presentation
  筑波大学自然系学系棟Ｄ
- Year and Date
  2016-03-07
- Data Source
  KAKENHI-PROJECT-15K04897
[Presentation] Homomorphisms on vector-valoued Banach function algebras2016
- Author(s)
  Osamu Hatori, Shiho Oi and Hiroyuki Takagi
- Organizer
  米沢数学セミナー
- Place of Presentation
  山形大学工学部（山形県米沢市）
- Data Source
  KAKENHI-PROJECT-26400080
[Presentation] 正則関数環の間の保存写像2015
- Author(s)
  高木啓行
- Organizer
  信州数学セミナー
- Place of Presentation
  信州大学理学部
- Year and Date
  2015-12-06
- Data Source
  KAKENHI-PROJECT-15K04897
[Presentation] 直積空間と等長作用素2013
- Author(s)
  高木啓行・古清水大直
- Organizer
  つくばセミナー
- Place of Presentation
  筑波大学
- Data Source
  KAKENHI-PROJECT-23540193
[Presentation] Real-linear isometries between subspaces of continuous functions2011
- Author(s)
  H. Koshimizu, T. Miura, H. Takagi and S.-E. Takahasi
- Organizer
  Research on preserver problems concerning to Banach algebras and its applications
- Place of Presentation
  京大・数理研
- Data Source
  KAKENHI-PROJECT-23540193
[Presentation] Ulam type stability problems for alternative homomorphisms2011
- Author(s)
  S.-E. Takahasi, T. Miura, H. Takagi and K. Tanahashi
- Organizer
  第20回関数空間セミナー
- Place of Presentation
  北大・理
- Data Source
  KAKENHI-PROJECT-23540193
[Presentation] シフト作用素に関する2・3の注意2009
- Author(s)
  古清水大直,高木啓行
- Organizer
  つくばセミナー
- Place of Presentation
  筑波大学
- Year and Date
  2009-03-10
- Data Source
  KAKENHI-PROJECT-18540167
[Presentation] バナッハ空間でシフト作用素を考える2007
- Author(s)
  高木啓行
- Organizer
  つくばセミナー
- Place of Presentation
  筑波大学
- Year and Date
  2007-11-21
- Data Source
  KAKENHI-PROJECT-18540167
[Presentation] バナッハ空間でシフト作用素を考える2007
- Author(s)
  高木啓行
- Organizer
  バナッハ環セミナー
- Place of Presentation
  筑波大学
- Year and Date
  2007-11-21
- Data Source
  KAKENHI-PROJECT-18540167
[Presentation] シフト作用素の一般化について2006
- Author(s)
  高木啓行
- Organizer
  関数環研究集会
- Place of Presentation
  岩手医科大学
- Year and Date
  2006-12-03
- Data Source
  KAKENHI-PROJECT-18540167
[Presentation] 直積空間上のシフト作用素
- Author(s)
  高木啓行, 古清水大直
- Organizer
  第2回山陰基礎論・解析学研究集会
- Place of Presentation
  鳥取県米子市国際ファミリープラザ
- Year and Date
  2015-01-24 – 2015-01-25
- Data Source
  KAKENHI-PROJECT-23540193
[Presentation] 保存問題における関数空間上の等距離写像について
- Author(s)
  高木啓行、古清水大直
- Organizer
  山陰基礎論・解析学セミナー
- Place of Presentation
  米子高専
- Data Source
  KAKENHI-PROJECT-23540193

1. HATORI Osamu (70156363)

# of Collaborated Projects: 6 results

# of Collaborated Products: 5 results
2. MATSUGU Yasuo (60020682)

# of Collaborated Projects: 4 results

# of Collaborated Products: 0 results
3. MIURA Takeshi (90333989)

# of Collaborated Projects: 4 results

# of Collaborated Products: 9 results
4. 板谷信敏 (70047455)

# of Collaborated Projects: 3 results

# of Collaborated Products: 0 results
5. TAKAHASI Sin-ei (50007762)

# of Collaborated Projects: 2 results

# of Collaborated Products: 7 results
6. IZUCHI Keiji (80120963)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
7. UEKI Sei-Ichiro (70512408)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
8. 浅田明 (00020652)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
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27. 古清水大直 (50713939)

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TAKAGI Hiroyuki 高木 啓行

高木 啓行 タカギ ヒロユキ

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荷重合成作用素の保存構造の研究Principal Investigator

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Studies on structures and isometries of commutative Banach algebrasPrincipal Investigator

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Studies on composition operators and spectrum-preserving mapsPrincipal Investigator

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関数空間上の荷重合成作用素についてPrincipal Investigator

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[Book] フーリエ解析入門(プリンストン解析学講義I)2007

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[Book] 『翻訳書』スタイン&シャカルチ「フーリエ解析入門」(プリンストン解析講義)2007

TAKAGI Hiroyuki 高木啓行

高木啓行タカギヒロユキ