Deformation of Bargmann-Fock representation in non-commutative probability theory
| Project/Area Number |
16K05175
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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 | Aichi University of Education |
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Principal Investigator |
Asai Nobuhiro 愛知教育大学, 教育学部, 教授 (60399029)
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| Project Period (FY) |
2016-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | フォック空間 / 非可換確率論 / 直交多項式論 / 確率分布 / B型ガウス・ポアソン作用素 / 変形フォック空間 / 直交多項式 / 離散確率分布 / 変形ガウス型作用素 / ポアソン型作用素 / 変形マイクスナー分布 / 荷重フォック空間 / 量子確率論 / バーグマン測度 / 関数解析学 / 確率論 |
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| Outline of Final Research Achievements |
We considered deformations of the Bargmann-Fock space, Gaussian/Poisson operators, and their probability distributions in terms of non-commutative probabilistic approach. (1) The radial Bargmann density function associated with the Fock space of type B is explicitly obtained. (2) Gaussian-Poisson type operators on the type B space are introduced. As a result, we showed that a q2-Meixner class of probability measures can be treated within the framework of type B. (3) We constructed a weighted q-Fock space and presented unknown and non-trivial examples in previous works.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究において，従来のフォック空間ならびにガウス・ポアソン型作用素の変形・補間理論の拡張により，確率論や非可換確率論では馴染みの薄い非自明な確率分布とより強い非可換性との関係解明への足掛かりになっていることが意義深い．
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Report
(6 results)
Research Products
(30 results)
