2004 Fiscal Year Final Research Report Summary
Research on Functional Analysis and Mathematical theory of Feynman path integrals.
| Project/Area Number |
15540184
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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 | Gakushuin University. |
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Principal Investigator |
FUJIWARA Daisuke Gakushuin Univ., Dept. of Math., Prof., 理学部, 教授 (10011561)
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| Co-Investigator(Kenkyū-buntansha) |
YAJIMA Kenji Gakushuin Univ., Dept. of Math., Prof., 理学部, 教授 (80011758)
KATASE Kiyoshi Gakushuin Univ., Dept. of Math., Prof., 理学部, 教授 (70080489)
MIZUTANI Akira Gakushuin Univ., Dept. of Math., Prof., 理学部, 教授 (80011716)
WATANABE Kazuo Gakushuin Univ., Dept. of Math., Assist., 理学部, 助手 (90260851)
SHIMOMURA Akihiro Gakushuin Univ., Dept. of Math., Assist., 理学部, 助手 (00365066)
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| Project Period (FY) |
2003 – 2004
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| Keywords | Feynman path integrals / Oscillatory integrals / Schrodinger equation / Stationary phase / Selfajoint operator / Quantum mechanics / WKB-method / path integrals |
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| Research Abstract |
1. Fujiwara tried to give mathematically rigorous treatment of Feynman path integrals. He proved an improved remainder estimate of stationary phase method for oscillatory integrals over a space of large dimension. And he make the discussion of Kumano-go's results on convergence of Feynman path integrals. He also proved a new formula for the second term of the semi-classical asymptotics of Feynman path integrals.
2. Yajima got results on spectrum and scattering properties of Nelson model, which is a simplified model of non-relativistic QED. He also succeeded in proving that every solution of Schrodinger equation with potentials which grow of oder O(|x|^m), m > 2 at the infinity gains, at almost every t, differentiability of order 1/m compared with its initial value.
3. Watanabe made research on solutions of PDE with dispersive type. In the joint with T. Suzuki and T. Kobayashi he also proved interface regularity of solutions to the system of Maxwell-Stokes equations. He also discussed.
4. Shimomura discussed large time behaviour of solutions to non-linear Schrodinger equations. He succeeded in finding a quite a fine property of solutions which is not foreseen from mere growth order of nonlinear term. Shimomura also proved smoothing effects of time local solution to non-linear Schrodinger equation with electro-magnetic potential.
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Research Products
(31 results)
