Stochastic analysis and semi-classical problem in infinite dimensional spaces
| Project/Area Number |
15540169
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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 |
Basic analysis
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| Research Institution | Osaka University |
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Principal Investigator |
AIDA Shigeki Osaka University, Graduate school of engineering science, Professor, 大学院・基礎工学研究科, 教授 (90222455)
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| Co-Investigator(Kenkyū-buntansha) |
NAGAI Hideo Osaka University, Graduate school of engineering science, Professor, 大学院・基礎工学研究科, 教授 (70110848)
NAGAHATA Yukio Osaka University, Graduate school of engineering science, Research Associate, 大学院・基礎工学研究科, 助手 (50397725)
HINO Masanori Kyoto university, Graduate school of informatics, Associate Professor, 大学院・情報学研究科, 助教授 (40303888)
磯崎 泰樹 大阪大学, 大学院・理学研究科, 助手 (90273573)
桑江 一洋 熊本大学, 教育学部, 助教授 (80243814)
関根 順 大阪大学, 大学院・基礎工学研究科, 助教授 (50314399)
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| Project Period (FY) |
2003 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2005: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2004: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2003: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Keywords | Semi-classical limit / Stochastic analysis / Rough path analysis / Witten Laplacian / Log-Sobolev inequality / Path integral / Quantum_field theory / ループ空間 / 径路積分表示 / 推移確率 / シュレーディンガー作用素 / ラプラスの方法 / 弱ポアンカレ不等式 / ラブラスの方法 |
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| Research Abstract |
The results are as follows :
(1)We determine the limit of the lowest eigenvalue of a Schr"odinger operator on a Wiener space under semi-classical limit. This is the case where the coefficient operator of the Dirichlet form is identity operator. Also we extend the result to the case where the coefficient operator is variable case and the case of a Schr"odinger operator on a path space over a compact Riemannian manifold in a recent preprint. The points are to use a unitary transformation by an approximate ground state function and rough path analysis.
(2)We prove a weak Poincare inequality on a loop space over a compact Riemannian manifold by using the rough path analysis.
(3)We prove a weak Poincare inequality on a loop space over a compact Riemannian manifold by using the rough path analysis.
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Report
(4 results)
Research Products
(13 results)
