2005 Fiscal Year Final Research Report Summary
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)
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| Project Period (FY) |
2003 – 2005
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| Keywords | Semi-classical limit / Stochastic analysis / Rough path analysis / Witten Laplacian / Log-Sobolev inequality / Path integral / Quantum_field theory |
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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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Research Products
(8 results)
