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New development of analysis and geometry on convex cones

Research Project

Project/Area Number 20K03657
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12010:Basic analysis-related
Research InstitutionOsaka Metropolitan University (2022-2023)
Osaka City University (2020-2021)

Principal Investigator

Ishi Hideyuki  大阪公立大学, 大学院理学研究科, 教授 (00326068)

Project Period (FY) 2020-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2023: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2022: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywordsウィシャート分布 / 等質錐 / ジョルダン代数 / グラフィカルモデル / 可解リー群 / 連続ウェーブレット変換 / ヘッセ幾何 / 等質ケーラー多様体 / 等質ヘッセ領域 / ジーゲル・ヤコビ領域 / 軌道の方法 / コーダルグラフ / ベイズ統計 / 二重自己平行部分多様体 / ハルトークス領域 / 強可視的作用 / ベルグマン核 / 等質凸領域 / リース超函数 / リース超関数 / 正定値実対称行列 / ヘッセ計量
Outline of Research at the Start

等質錐の研究において申請者が導入した「行列実現の方法」を拡張し,応用数学においても重要なコーダルグラフィカルモデルを含む広いクラスの凸錐について,幾何と解析を展開する.具体的には,行列式の巾乗や対数のヘッシアンに関係する調和解析や微分幾何を,それらの構造を不変にする群作用に着目しながら考察する.等質錐と関連する空間(等質ジーゲル領域,等質ヘッセ領域)についても研究を広さと深さの両方に理論を発展させる.数理統計や凸計画法を含む様々な分野への応用も追究する.非可換調和解析の研究で培った群論的視点からのアプローチが本研究の特色である.

Outline of Final Research Achievements

The study of homogeneous cones is not only related to various areas of pure mathematics such as representation theory, complex geometry, and harmonic analysis, but also applied to multivariate analysis and convex optimization.
The theory of homogeneous cones is reorganized efficiently by the method of matrix realization developed by myself. In this research project, we obtained integral formulas of the Gamma type and their applications as well as various results about differential geometry over related spaces. Moreover, we prove some general theorems in representation theory of solvable Lie groups and harmonic analysis,
which are intrinsically related to the theory of convex cones.

Academic Significance and Societal Importance of the Research Achievements

本研究で得られた積分公式や幾何学的定理は,それ自身の数学的な価値だけでなく,数理統計や凸最適化への応用にも重要な意義がある.とくに,与えられた多次元データに最も適合する置換対称性をベイズ統計を用いて探索するというモデル選択問題において,ボトルネックとなる積分を,群の表現論と対称錐上の調和解析を用いて正確かつ簡単に計算することができたことは大きな成果であった.

Report

(5 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • Research Products

    (36 results)

All 2024 2023 2022 2021 2020 Other

All Int'l Joint Research (11 results) Journal Article (10 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 7 results,  Open Access: 2 results) Presentation (14 results) (of which Int'l Joint Research: 7 results,  Invited: 6 results) Funded Workshop (1 results)

  • [Int'l Joint Research] アンジェ大学(フランス)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] ワルシャワ工科大学(ポーランド)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] スファックス大学(チュニジア)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] University of Angers(フランス)

    • Related Report
      2022 Research-status Report
  • [Int'l Joint Research] Warsaw University of Technology(ポーランド)

    • Related Report
      2022 Research-status Report
  • [Int'l Joint Research] Sfax University(チュニジア)

    • Related Report
      2022 Research-status Report
  • [Int'l Joint Research] University of Angers(フランス)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] Warsaw University of Technology(ポーランド)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] Sfax University(チュニジア)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] University of Angers/University of Lorrainze(フランス)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] Warsaw University of Technology(ポーランド)

    • Related Report
      2020 Research-status Report
  • [Journal Article] Open orbits and primitive zero ideals for solvable Lie algebras2024

    • Author(s)
      Ali Baklouti, Hideyuki Ishi
    • Journal Title

      Forum Mathematicum

      Volume: 36 Issue: 3 Pages: 571-584

    • DOI

      10.1515/forum-2022-0307

    • Related Report
      2023 Annual Research Report
  • [Journal Article] On a Concrete Realization of Simply Connected Complex Domains Admitting Homogeneous Kaehler Metrics2024

    • Author(s)
      Hideyuki Ishi
    • Journal Title

      Springer Proceedings in Mathematics and Statistics

      Volume: 447 Pages: 261-272

    • DOI

      10.1007/978-981-99-9506-6_9

    • ISBN
      9789819995059, 9789819995066
    • Related Report
      2023 Annual Research Report
  • [Journal Article] Doubly autoparallel structure and curvature integrals: Applications to iteration complexity for solving convex programs2023

    • Author(s)
      Atsumi Ohara,Hideyuki Ishi and Takashi Tsuchiya
    • Journal Title

      Information Geometry

      Volume: 7 Issue: S1 Pages: 555-586

    • DOI

      10.1007/s41884-023-00116-x

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Mathematical considerations for evaluating X-ray beam size in micro-XRF analysis2023

    • Author(s)
      Masanori Nakae; Tsugufumi Matsuyama; Hideyuki Ishi; Kouichi Tsuji
    • Journal Title

      X-Ray Spectrometry

      Volume: Early View Issue: 6 Pages: 290-302

    • DOI

      10.1002/xrs.3325

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Model selection in the space of Gaussian models invariant by symmetry2022

    • Author(s)
      Piotr Graczyk, Hideyuki Ishi, Bartosz Kolodziejek, Helene Massam
    • Journal Title

      Annals of Statistics

      Volume: 50 Issue: 3 Pages: 1747-1774

    • DOI

      10.1214/22-aos2174

    • URL

      https://ocu-omu.repo.nii.ac.jp/records/2020513

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Graphical Gaussian Models Associated to a Homogeneous Graph with Permutation Symmetries2022

    • Author(s)
      Piotr Graczyk, Hideyuki Ishi, Bartosz Kolodziejek
    • Journal Title

      Physical Sciences Forum

      Volume: 5 Pages: 20-20

    • DOI

      10.3390/psf2022005020

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On Gaussian Group Convex Models2021

    • Author(s)
      Hideyuki Ishi
    • Journal Title

      Springer Lecuture Notes in Computer Science

      Volume: 2021 Pages: 256-264

    • DOI

      10.1007/978-3-030-80209-7_29

    • ISBN
      9783030802080, 9783030802097
    • URL

      https://ocu-omu.repo.nii.ac.jp/records/2020669

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Continuous Wavelet Transforms for Vector-Valued Functions2021

    • Author(s)
      Hideyuki Ishi and Kazuhide Oshiro
    • Journal Title

      Springer Lecture Notes in Computer Science

      Volume: 2021 Pages: 331-339

    • DOI

      10.1007/978-3-030-80209-7_37

    • ISBN
      9783030802080, 9783030802097
    • URL

      https://ocu-omu.repo.nii.ac.jp/records/2020670

    • Related Report
      2021 Research-status Report 2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] The compression semigroup of the dual Vinberg cone2021

    • Author(s)
      Hideyuki Ishi and Khalid Koufany
    • Journal Title

      Springer Proceedings in Mathematics and Statistics

      Volume: 366 Pages: 123-136

    • DOI

      10.1007/978-3-030-78346-4_8

    • ISBN
      9783030783457, 9783030783464
    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On Gaussian Group Convex Models2021

    • Author(s)
      Hideyuki Ishi
    • Journal Title

      Springer Lecuture Notes in Computer Science

      Volume: -

    • Related Report
      2020 Research-status Report
  • [Presentation] ジョルダン代数と情報幾何2023

    • Author(s)
      伊師英之
    • Organizer
      千里山幾何学研究会
    • Related Report
      2023 Annual Research Report
    • Invited
  • [Presentation] The Jorgensen set for transformation exponential families2023

    • Author(s)
      Hideyuki Ishi
    • Organizer
      The Fourth International Symposium on Information Geometry and Affine Differential Geometry
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] The Gamma integral formulas for certain non-homogeneous convex cones2023

    • Author(s)
      Hideyuki Ishi
    • Organizer
      Workshop on classical analysis and applications VI & Colloguim in honor of David Bekolle
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 色付き等質グラフからの等質錐の構成2022

    • Author(s)
      伊師英之
    • Organizer
      日本数学会2022年秋季総合分科会函数解析学分科会
    • Related Report
      2022 Research-status Report
  • [Presentation] Complex domains admitting homogeneous Kahler metrics2022

    • Author(s)
      Hideyuki Ishi
    • Organizer
      HAYAMA Symposium on Complex Analysis in Several Variables XXIII
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research
  • [Presentation] On Gaussian group convex models2021

    • Author(s)
      Hideyuki Ishi
    • Organizer
      5th Conference on Geometric Science of Information
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] Continuous wavelet transforms for vecor-valued functions2021

    • Author(s)
      Hideyuki Ishi and Kazuhide Oshiro
    • Organizer
      5th Conference on Geometric Science of Information
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] 調和解析の問題2021

    • Author(s)
      伊師英之
    • Organizer
      RIMS研究集会「複素幾何学の諸問題II」
    • Related Report
      2021 Research-status Report
  • [Presentation] On algebraic structure in decomposable graphical Gaussian models with group symmetry2021

    • Author(s)
      伊師英之
    • Organizer
      OCAMI研究集会「統計的推測理論への幾何学的アプローチ」
    • Related Report
      2021 Research-status Report
  • [Presentation] On normalizing constants of chordal graphical Gaussian models with group symmetry2021

    • Author(s)
      Hideyuki Ishi
    • Organizer
      14th International Conference of the ERCIM WG on Computational and Methodological Statistics
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] ベクトル値函数の連続ウェーブレット変換2021

    • Author(s)
      伊師英之, 大城和秀
    • Organizer
      日本数学会2022年度年会函数解析学分科会一般講演
    • Related Report
      2021 Research-status Report
  • [Presentation] Berezin-Wallach-Gindikin-Jorgensen 集合について2021

    • Author(s)
      伊師英之
    • Organizer
      第16回代数・幾何・解析セミナー
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] 置換対称性をもつガウシアンモデルについて2021

    • Author(s)
      伊師英之
    • Organizer
      ワークショップ「第二回 分布族と離散集合の幾何とその周辺」
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] Cholesky structures on matrices and their applications2020

    • Author(s)
      Hideyuki Ishi
    • Organizer
      Mathematical Methods of Modern Statistics 2
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Funded Workshop] 7th Tunisian-Japanese Conference "Geometric and Harmonic Analysis on Homogeneous Spaces and Applications"2023

    • Related Report
      2023 Annual Research Report

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Published: 2020-04-28   Modified: 2025-01-30  

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