2000 Fiscal Year Final Research Report Summary
Research in Functional Analsys and Mathematical theory of Feynman path integrals.
| Project/Area Number |
11640180
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Gakushuin University |
|---|
Principal Investigator |
FUJIWARA Daisuke Gakushuin Univ.Dept.of Math.Prof., 理学部, 教授 (10011561)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
MIZUTANI Akira Gakushuin Univ.Dept.of Math.Prof., 理学部, 教授 (80011716)
KATASE Kiyoshi Gakushuin Univ.Dept.of Math.Prof., 理学部, 教授 (70080489)
KURODA Shigetoshi Gakushuin Univ.Dept.of Math.Prof., 理学部, 教授 (20011463)
SUGANO Satoko Gakushuin Univ.Dept.of Math.Assist., 理学部, 教授 (50316931)
WATANABE Kazuo Gakushuin Univ.Dept.of Math.Assist., 理学部, 助手 (90260851)
|
|---|
| Project Period (FY) |
1999 – 2000
|
| Keywords | Feynman path integrals / Oscillatory integrals / Schrodinger equation / Stationary phase / Selfajoint operator / Quantum mechanics / WKB-method / path integrals |
|---|
| Research Abstract |
1. Fujiwara tried to give mathematically rigorous treatment of Feynman path integrals. It may seem possible to get a new proof of Kumanogo-Taniguchi theorem for actions with electro-magnetic fields if we cleverly conbine N.Kumanogo's method to that of our work which were published in 1997. Fujiwara wrote a textbook published by Springer Verlarg Tokyo in 1999. The english translation of the title is "Mathematical Method of Feynman path integrals".
2. S.T.Kuroda together with P.Kurasov of Stockholm University showed that the Krein's formula describing relations of self-adjoint extension of two operators can be understood as resolvent equation between two operators. And they dicussed H_∈-perturbation theory.
3. Mizutani studied finite element methods for parabolic nonlinear partial differential equations.
4. Watanabe togeher with Kurasov of Stockholm Univ. studied H_4 realization of selfadjoint extension of operators.
5. Sugano together with Kurata of Metropolitan Univ. studied fundamental solutions of uniformly elliptic operators with potentials in a class of functions which is a generalization of the class of positive polynomials. They suceeded in proving their fundamental solutions show good behviour in the weighted L^p space and Morrey classes. Using these facts, they proved a good estimates of distribution of eigen values and sharp information for order of decay of eigen functions of their elliptic operators.
|
