2020 Fiscal Year Final Research Report
Harmonic analysis on convex cones and its applications
| Project/Area Number |
16K05174
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Osaka City University (2019-2020)
Nagoya University (2016-2018) |
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Principal Investigator |
Hideyuki Ishi 大阪市立大学, 大学院理学研究科, 教授 (00326068)
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| Project Period (FY) |
2016-04-01 – 2021-03-31
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| Keywords | ウィシャート分布 / 正定値対称行列 / 等質錐 / グラフィカルモデル / ヘッセ幾何 / 可解リー群 / リース超函数 |
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| Outline of Final Research Achievements |
A homogeneous cone is an open convex cone on which a linear Lie group acts transitively. It is knwon that one can develop rich analysis on the homogeneous cones as well as convex cones appearing in the chordal graphical models. In this research project, I find a new wide class of convex cones containing both the homogeneous cones and chordal graphical models, and I investigate harmonic analysis on these cones. Relating to the new theory, I obtain results in various areas such as representation theory, real analysis, complex analysis, mathematical statistics, optimization, and information geometry.
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| Free Research Field |
非可換調和解析，表現論，複素解析，多変量解析
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| Academic Significance and Societal Importance of the Research Achievements |
本研究は，線型な制約条件を課した正定値実対称行列の研究が主題であり，数理統計（とくに多変量正規分布の分散の推定問題）や最適化法（半正定値計画法の一般化）に様々な応用がある．実際，本研究で考察してきた問題はそれらの分野から刺激や動機づけを得て取り組んできたものが多い．そして研究成果を得る過程で，統計学者や応用数学者との共同研究を活発に行い，コミュニティを超えたネットワークを構築できたことも大きな収穫であった．
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