| Project/Area Number |
10440037
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | THE UNIVERSITY OF TOKYO |
|---|
Principal Investigator |
KATAOKA Kiyoomi Graduate School of Mathematical Sciences, THE UNIVERSITY OF TOKYO, Professor, 大学院・数理科学研究科, 教授 (60107688)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
YAJIMA Kenji Graduate School of Mathematical Sciences, THE UNIVERSITY OF TOKYO, Professor, 大学院・数理科学研究科, 教授 (80011758)
MATANO Hiroshi Graduate School of Methematical Sciences, THE UNIVERSITY OF TOKYO, Professor, 大学院・数理科学研究科, 教授 (40126165)
OSHIMA Toshio Graduate School of Methematical Sciences, THE UNIVERSITY OF TOKYO, Professor, 大学院・数理科学研究科, 教授 (50011721)
YAMAMOTO Masahiro Graduate School of Mathematical Sciences, THE UNIVERSITY OF TOKYO, Associate Professor, 大学院・数理科学研究科, 助教授 (50182647)
FUNAKI Tadahisa Graduate School of Mathematical Sciences, THE UNIVERSITY OF TOKYO, Professor, 大学院・数理科学研究科, 教授 (60112174)
堤 誉志雄 東京大学, 大学院・数理科学研究科, 助教授 (10180027)
|
|---|
| Project Period (FY) |
1998 – 1999
|
| Project Status |
Completed (Fiscal Year 1999)
|
| Budget Amount *help |
¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1999: ¥1,800,000 (Direct Cost: ¥1,800,000)
|
|---|
| Keywords | microlocal analysis / second microlocal analysis / Lagrangian / microfunctions / Mellin transformations / pseudo-differential operators / holomorphic functions / boundary values / 第二超局所解析 / 偏微分方程式 / 佐藤超関数 / コロンボ超関数 / FBI変換 |
|---|
| Research Abstract |
Our researches concerning non-linear analysis in our project had almost no progress because we encountered a unexpected difficulties. However our researches concerning linear analysis had a remarkable progress due to KATAOKA's group ; in particular, the second microlocal analysis and an elementary construction of the microlocal theory of systems of equations.
1. In the microlocal analysis, it is indispensable to employ expressions of singular solutions or kernel functions by boundary values of pseudodifferential operators. Concerning these expressions, KATAOKA's group obtained a necessary and sufficient condition on growth orders of lower order terms of formal symbols of pseudo-differential operators for taking boundary values. This result was applied to the analysis of microlocal solutions of some Fuchsian type equations. Further this result is deeply connected to the theory of small second hyperfunctions in the second microlocal analysis.
2. KATAOKA's group succeeded in obtaining an integral formula of Mellin's type for holomorphic functions with any growth order at the corner in one-dimensional angled domains ; the main idea is to tilte the integral paths. Such a formula was indispensable for extending FUNAKOSHI's resullt on second microlocal analysis along Lagrangian submanifolds.
|
