1996 Fiscal Year Final Research Report Summary
Comprehensive Study of Functional and Real Analysis
| Project/Area Number |
07304014
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 総合 |
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| Research Field |
解析学
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| Research Institution | Science University of Tokyo (1996)
The University of Tokyo (1995) |
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Principal Investigator |
KOMATSU Hikosaburo Science University of Tokyo, Faculty of Science, Professor, 理学部第一部, 教授 (40011473)
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| Co-Investigator(Kenkyū-buntansha) |
TAJIMA Shinichi Niigata University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (70155076)
FUJII Masatoshi Osaka Kyoiku University, Faculty of Education, Professor, 教育学部, 教授 (10030462)
TAKENAKA Shigeo Okayama University of Science, Faculty of Science, Professor, 理学部, 教授 (80022680)
NAKAZI Takahiko Hokkaido University, Graduate, School of Science, Professor, 大学院・理学研究科, 教授 (30002174)
YONEDA Kaoru Osaka Prefecture University, College of Integrated Arts and Sciences, Professor, 総合科学部, 教授 (80079029)
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| Project Period (FY) |
1995 – 1996
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| Keywords | functional analysis / real analysis / theory of real variables / function spaces / operator theory / operator algebras / represetation theory and harmonic analysis / partial differential equations |
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| Research Abstract |
This is a comprehensive research project involving all active mathematicians in the fields of Functional and Real Analysis. The aim is to have a proper perspective of recent progress in these fields in Japan as well as in the world so that coordinated research activities are possible for the future. For this purpose we made five groups according to the subjects.Each group conducted standing seminars and a nationwide meeting each year. The Investigators met three times every year in order to maintain close correspondence between the groups, and organized a joint symposium each year.
In view of this character of the research project it is difficult to summarize our results in a few words but the following could be said. Until recently both Functional Analysis and Real Analysis are so much specialized that many results are profound but interest only few specialists of particular fields. However, we are having now a new trend in which those profound results are applied to an unexpected problem to make a breakthrough of a field which is stagnated for a long time. Our research project has promoted this desirable tendency of researches.
For example, some of the function spaces appearing in Real Analysis have been proved to play a essential role in the theory of partial differential equations, although they were introduced only by theoretical necessity in Real Analysis. Toeplitz operators, which were introduced as examples of operators not equivalent to multiplications, are recognized as the same as pseudodifferential operators, and have found applications to the representation theory of Lie groups. Many approaches have been made for non-linear problems. A new lights was shed on the classical WKB method of perturbation.
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