2013 Fiscal Year Final Research Report
Quantum probabilistic approach to the Segal-Bargmann transform and infinitely divisible laws
| Project/Area Number |
23540131
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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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, 准教授 (60399029)
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| Co-Investigator(Renkei-kenkyūsha) |
KUBO Izumi 広島大学, 大学院・理学研究科, 名誉教授 (70022621)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 量子確率論 / 直交多項式 / シーガル・バーグマン変換 / ブレンケ型母関数 / ｑ類似 |
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| Research Abstract |
From the point of multiplicative renormalization method, we examined the Brenke-Chihara problem, which is to determine all orthogonal polynomials associated with the Brenke type generating functions. As a result, all of the Jacobi-Szego parameters and q-hypergeometric series representations for all MRM-factors are obtained, explicitly. Our paper was published from IDAQP, an international mathematics journal. We have begun to consider if there would exist q-Fourier or q-Segal-Bargmann transforms and associated convolution products in a meaningful way from the quantum(algebraic) probabilistic view point.
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