1994 Fiscal Year Final Research Report Summary
Comprehensive study of real analysis and functional analysis
| Project/Area Number |
05302008
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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 | KYOTO UNIVERSITY |
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Principal Investigator |
HIRAI Takeshi Kyoto Univ.Fac.Sci.Prof., 理学部, 教授 (70025310)
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| Co-Investigator(Kenkyū-buntansha) |
KOMATSU Hikosaburo Univ.of Tokyo Prof., 大学院・数理科学研究科, 教授 (40011473)
TAKEMOTO Hideo Miyagi Education Univ.Prof., 教育学部, 教授 (00004408)
MINEMURA Katsuhiro Japan Womans Univ.Prof., 理学部, 教授 (20060684)
OHARU Shinnosuke Hiroshima Univ.Prof., 理学部, 教授 (40063721)
MIYACHI Akihiko Hitotsubashi Univ.Prof., 社会学部, 教授 (60107696)
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| Project Period (FY) |
1993 – 1994
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| Keywords | real analysis / functional analysis / function space / representation / operator algebra / function algebra / harmonic analysis / partial differential equation |
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| Research Abstract |
Our studies were mainly carried out according to the following five groups : Real Analysis and Commutative Harmonic Analysis, Function Spaces and Operators, Group Representations and Non-commutative Harmonic Analysis, Operator Algebras and Function Algebras, Functional Analytic Studies on Partial Differential Equations. We pick up some of the works of our members. In the first group, Morrey Spaces, BMO spaces, Besov spaces and operators on them were studied. A.Miyachi studied the spaces defined by means of sharp max functions, and problems on extension of functions on a domain and those on products of functions. S.Igari et al.studied Banach spaces and Banach algebras.
F.Takeo studied Hausdorff dimension of fractal sets. S.Oharu et al.studied semigroups of non-linear oparators coming from non-linear evolution equations. Concerning this subject, they obtained final results on non-linear perturbations of analytic semigroups, adjoint semigroups etc. In the third group, representation theories of infinite dimensional Lie groups and quantum groups were studied. The works of M.Kashiwara and those of M.Jinbo are remarkable. T.Oshima, T.Kobayashi, H.Yamashita et al.studied representations of semisimple Lie groups and harmonic analysis on semisimple symmetric spaces. T.Hirai studied the construction of irreducible unitary representations of infinite discrete groups and the decomposition of their regular representations, and further Howe type duality between the infinite symmetric group and groups of diffeomorphisms on manifolds. Representations of Lie super-algebras were studied by K.Nishiyama et al.
For partial differential equations, construction and expression of their solutions were studied by T.Kawai et al.H.Komatsu showde that his abstract Laplace transform can be applied to get rapidly the classical expression of the solutions of some explicit differential equations.
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