1994 Fiscal Year Final Research Report Summary
CO-operative Research on Functional Analysis, Real Analisis, and Partial Diffential Equations
| Project/Area Number |
04302007
|
|---|
| Research Category |
Grant-in-Aid for Co-operative Research (A)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
解析学
|
|---|
| Research Institution | Gakushuin University |
|---|
Principal Investigator |
KURODA Shige Toshi Gakushuin Univ, Fac Sci, Prof, 理学部, 教授 (20011463)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
KOMATSU Hikosaburo Univ.of Tokyo, Dept Math Sci, Prof, 数理科学研究科, 教授 (40011473)
MURAMATSU Toshinobu Univ.of Tsukuba, Math Prof, 数学系, 教授 (60027365)
YAJIMA Kenji Univ.of Tokyo, Dept Math Sci, Prof, 数理科学研究科, 教授 (80011758)
MURATA Minoru Tokyo Inst.Tech, Fac Sci, Prof, 理学部, 教授 (50087079)
IGARI Satoru Tohoku Univ, Fac Sci, Prof, 理学部, 教授 (50004289)
|
|---|
| Project Period (FY) |
1992 – 1994
|
| Keywords | Harmonic Analysis / Partial Differential Equation / Fourier Analysis / Function Space / Positive Solution / Scattering Theory |
|---|
| Research Abstract |
This research project aimed at investigating problems related to three disciplines mentioned in the title in the spirit of co-operative work and from a unique viewpoint. Results obtained during three years will be itemized below.
1.Methods of Functional and Real Analysis applied to Partial Differential Equations(PDE). Properties of solutions of nonlinear PDE are investigated by these tools and using various results on function spaces. 2.Harmonic Analysis and Complex Analysis. Results are obtained on degenerate elliptic PDE on strongly pseudo-convex domains. These results have some connection with geometry and the theory of probability.
3.Wavelet Analysis. Wavelets theory and related theory of Wilson basis are applied to the prob-lem of asymptotic distribution of eigenvalues of Schrodinger operators and the boundedness of pseudo-differential operators.
4.Asymptotic Analysis, Mathematical Physics.
(1)Application of Asymptotic Analysis to Mathematical Physics of quantum theory.
(2)Various results on scattering theroy are obtaind, notably L^P boundedness of wave operators.
5.Structure of Positive Solutions.Broard investigations are made on the concrete structure of positive solutions of 2nd order parabolic and elliptic PDEs on non relatively compact domains. Here, the investigation is also related to potential theory, geometry, and the theory of probability.
These results manifest clearly strong ties which exist between Rear Analysis, Fourier Analysis, Linear and nonliner PDEs, and Mathematical Physics.Each of these disciplines has certainly its own history of development. We feel that, while pushing researches in each field deeper and deeper, project of co-operative researches from overall viewpoints are much necessary and should be pushed further.
|
