| Project/Area Number |
20540145
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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 | Hiroshima University |
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Principal Investigator |
KUBO Izumi Hiroshima University, 大学院・理学研究科, 名誉教授 (70022621)
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| Co-Investigator(Kenkyū-buntansha) |
IWATA Koichiro 広島大学, 大学院・理学研究科, 准教授 (20241292)
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| Co-Investigator(Renkei-kenkyūsha) |
YAGUCHI Hirotake 三重大学, 教育学部, 教授 (40157970)
SAITO Kimiaki 名城大学, 理工学部, 教授 (90195983)
ASAI Nobuhiro 愛知教育大学, 教育学部, 准教授 (60399029)
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| Research Collaborator |
IKEDA Satoshi 宮崎大学, 工学部, 准教授 (70282796)
NAKATA Toshio 福岡教育大学, 教育学部, 教授 (10304693)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 確率論 / 確率解析 / 白色雑音 / 数理物理 / カオス / 直交多項式 / 母関数 / 白色雑音系 / 解析学 / 直交多項式系 / 特殊関数 / 直行多項式系 |
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| Research Abstract |
Inspired by the multiplicative renormalization method (MRM) in white noise analysis, we have researched generating functions of orthogonal polynomials of probability measures by using MRM, systematically. It is a difficult problem to determine MRM-applicable measures. Generating functions of some classical orthogonal polynomials and of recently researching ones are obtained very naturally. Moreover, we found new classes of orthogonal polynomials and generating functions. Further, we researched structures of those classes.
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