| Project/Area Number |
62302002
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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 | Hokkaido University |
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Principal Investigator |
ANDO Tsuyoshi Hokkaido University, Research Institute of Applied Electricity, 応用電気研究所, 教授 (10001679)
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| Co-Investigator(Kenkyū-buntansha) |
MURAMATSU Toshinobu Tsukuba University, Mathematics, 数学系, 教授 (60027365)
SHINYA Hitoshi Ritsumeikan University, Faculty of Science and Technology, 理工学部, 教授 (70036416)
SAKA Koichi Akita University, Faculty of Education, 教育学部, 教授 (20006597)
SAKAI Shoichiro Nihon University, Faculty of Arts and Sciences, 文理学部, 教授 (30130503)
OHYA Masanori Tokyo University of Science, Faculty of Science and Technology, 理工学部, 教授 (90112896)
熊原 啓作 鳥取大学, 教養部, 教授 (60029486)
長田 尚 大阪教育大学, 教育学部, 教授 (00030338)
越 昭三 北海道大学, 理学部, 教授 (40032792)
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| Project Period (FY) |
1987 – 1988
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| Project Status |
Completed (Fiscal Year 1988)
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| Budget Amount *help |
¥16,000,000 (Direct Cost: ¥16,000,000)
Fiscal Year 1988: ¥8,000,000 (Direct Cost: ¥8,000,000)
Fiscal Year 1987: ¥8,000,000 (Direct Cost: ¥8,000,000)
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| Keywords | Functional analysis / Real analysis / Function spaces / Operator algebras / Operator / Harmonic analysis / Representation theory / 偏微分方程式 |
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| Research Abstract |
1. In the area of applications of function spaces, the notion of mahorization has proved useful for comparison of noncommutative operators, and applied to estimation of norems of operators. Various aspects of entropy in noncommutative dynamics been clarified by functional analytic methods. A classification of orbits in commutative dynamics was made and stability conditions were studied. A theory of evolutional eqations in general banach spaces was developed and applied to initial value problems of non-linear equations.
2. In the area of spplications of operator algebras, C^*-dnamics and quantum groups have been studied and applied to quantum mechanics. The Jones' indices were analyzed in detail. A new development of operator inequalities was established. In the field of function algebras, study of BMO functions by analytic methods was continued and applied to operators related to them. Further the Hardy-Orlicz classes were studied.
3. In the area of applications of real analysis, applications were investigated not only to measure theory, approximation theory and Fourier analysis but also to probility theory, pertial differential equations. In particular, Besov spaces on Riemannian manifolds were studied and applied to norm estimate of the solutions of were equations.
4. In the area of applications of representation theory and harmonic analysis, representations of infinite-dimensional groups and structure of lie superalgebras and Kac-Moody algebras are extensively studied. Remarkable results on the D-modules related algebraic gemetry were obtained.
5. In the area of applications of partial differential equations remarkable results in the fields of microlocal analysis and the boundary values problems of pseudo-differential equations were obtained. Eigenfunctions expansion of the schrodinger operator with a complex potential was successfully developed. In particular, a norm estimate of a pseudo-differential operator was obtained by a Besov methods.
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