2018 Fiscal Year Final Research Report
Deevelopment of Geometric and Microlocal Analysis
| Project/Area Number |
16K05221
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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 |
Mathematical analysis
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| Research Institution | University of the Ryukyus |
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Principal Investigator |
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| Research Collaborator |
ONODERA Eiji 高知大学
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Keywords | シーガル・バーグマン空間 / バーグマン変換 / エルミート展開 |
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| Outline of Final Research Achievements |
The purpose of this project is to study the analysis of functions on manifolds and mappings between manifolds, and the functional analysis related to microlocal analysis. We have some results concerned with functional analysis on the Bargmann-type integral transforms on the Euclidean spaces. The most important results of this project is to obtain the necessary and sufficient conditions on holomorphic gaussian functions on the complex Euclidean spaces so that they have creation and annihilation operators satisfying the canonical commutation relations and become generators of the complete orthonormal system on the Segal-Bargmann space, which is a reproducing-kernel Hilbert space of entire functions.
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| Free Research Field |
幾何解析
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| Academic Significance and Societal Importance of the Research Achievements |
本研究の成果は、これまでバーグマン型の積分変換やシーガル・バーグマン空間とは無関係に個別かつ具体的に研究されてきたいくつかの話題に関して、正統派と考えられるこれらの視点を導入し、従来よりも深い理解が得られた、あるいは、一般論を構築して従来の知見は特殊な具体例であることを示したものが多い。また、研究対象が、解析学だけでなく組合せ論の数え上げや特殊関数論などに一見無関係な話題と関連して発展する可能性がある。
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