1987 Fiscal Year Final Research Report Summary
Unified Research for Functional Analysis
| Project/Area Number |
60302006
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| Research Category |
Grant-in-Aid for Co-operative Research (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
解析学
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| Research Institution | Tokyo University of Mercantile Marine (1987)
The University of Tokyo (1985-1986) |
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Principal Investigator |
ITO Seizo Tokyo Univ. of Mercantile Marine; Professor, 商船学部, 教授 (40011423)
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| Co-Investigator(Kenkyū-buntansha) |
SUGIURA Mitsuo College of Arts and Science, Univ. of Tokyo; Professor, 教養学部, 教授 (50012258)
IGARI Satoru Fac. of Science, Tohoku Univ.; Professor, 理学部, 教授 (50004289)
WADA Junzo Sch. of Education, Waseda Univ.; Professor, 教育学部, 教授 (50063342)
UMEGAKI Hisaharu Fac. of Sci., Tokyo Science Univ.; Professor, 理学部, 教授 (00015992)
KURODA Shige Toshi Fac. of Sci., Gakushuin Univ.; Professor, 理学部, 教授 (20011463)
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| Project Period (FY) |
1985 – 1987
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| Keywords | Scattering theory / Schrodinger operator / Signal function / Operator algebra / Function algebra / Convexity theorem, Harmonic analysis / 調和解析,ユニタリ表現 |
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| Research Abstract |
By this project, important applications of methods of functional analysis to problems in various branches of analysis, have been studies and promoted. In spectral and scattering theory for Schrodinger operators, remarkable results have been obtained on micro-local estimate of resolvent, fundamental solutions, and the structure and asymptotic behavior of scattering matrices. As for the theory of function spaces, it is proved by the methods of functional-harmonic analysis, that the totality of signal functions bounded in certain sense is a Hilbert space with reproducing kernel. In the theory of operator algebras and function algebras, one-parameter groups of C^*-algebras have been investigated, and the theory of martingale has been introduced to Hardy spaces. In real analysis, a new convexity theorem in Lebesgue spaces with mixed norm has been obtained and applied to the estimates of spherical sum of Fourier transforms. As for the theory of unitary representations, harmonic analysis on semi-simple affine symmetric spaces has been investigated and the discrete series in the regular representation on such symmetric space has been determined.
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