Generalizations of infinite dimensional Laplacians, construction methods of stochastic processes and developments in quantum information analysis
| Project/Area Number |
21540151
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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 | Meijo University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
MATSUZAWA Tadato 名城大学, 理工学部, 教授 (20022618)
ICHIHARA Kanji 名城大学, 理工学部, 教授 (00112293)
MIMACHI Yuko (HARA Yuko) 名城大学, 理工学部, 准教授 (00218629)
NISHI Kenjiro 名城大学, 理工学部, 講師 (30076616)
OBATA Nobuaki 東北大学, 大学院・情報科学研究科, 教授 (10169360)
HIBINO Yuji 佐賀大学, 理工学部, 准教授 (50253589)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 無限次元ラプラス作用素 / 無限次元確率過程 / 確率過程構成法 / 量子情報解析 / Exotic Laplacian / レヴィ・ラプラシアンの一般化 / ホワイトノイズの高階微分 / チェサロヒルベルト空間 |
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| Research Abstract |
In this research, we considered a quantization and a new approach to a quantum information analysis by researching the infinite dimensional stochastic analysis jointly from major fields : probability theory, analysis, graph theory, number theory and computer science. Especially we succeeded in constructing the theory of higher order derivatives of white noise based on the stochastic analysis associated with exotic Laplacians defined by higher order Cesaro means of the second differentiation. It is a quite important progress and a creative point that a quantum information analysis in this direction can be constructed.
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Report
(4 results)
Research Products
(24 results)
