| Co-Investigator(Kenkyū-buntansha) |
MIWA Tetsuji Kyoto University, Research Institute for Mathematical Sciences, Associate Profes, 数理解析研究所, 助教授 (10027386)
KUSUOKA Shigeo Kyoto University, Research Institute for Mathematical Sciences, Associate Profes, 数理解析研究所, 助教授 (00114463)
NAKANISHI Noboru Kyoto University, Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (30027362)
KAWAI Takahiro Kyoto University, Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (20027379)
KASHIWARA Masaki Kyoto University, Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (60027381)
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| Research Abstract |
The purpose of this project is the study of infinite dimensional analysis and its application to the related fields, such as probability theory, infinite dimensional representation theory, theory of approximation, quantum field theory, statistic mechanics, fluid dynamics and so on. For this purpose, each member studied not only his own topic, but discussed each other to develop this project comprehensively. Studied main items are as follows, and in each of them we obtained considerable achievements :
1. Infinite dimensional measure theory : construction, extension, invariance, quasi-invariance, differentiability of measures.
2. Physical system with infinite degree of freedom, especially quantum field theory, statistical physics, fluid dynamics.
3. Representation of infinite dimensional groups and its application.
4. Stochastic process, Ergode theory, and Stochastic analysis on infinite dimensional manifolds.
5. Functional-analytic study of partial differential equations.
For instance, as to 1 we obtained several results on a) infinite dimensional infinitely decomposable measures, b) cyclic representation of shifts by infinite dimensional measures, c) norm-dependent characteristic function on a normed space. Also as to 2-5, many valuable researches have been done. As a result, 3 members of this project gave invited lectures in ICM 90.
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