| Co-Investigator(Kenkyū-buntansha) |
NISHISHIRAHO Toshihiko Faculty of Science,Ryukyu University,Professor, 理学部, 教授 (70044956)
KOMASTU Hikosaburo Department of Mathematical Sciences,The University of Tokyo,Professor, 大学院・数理科学研究科, 教授 (40011473)
HUJIWARA Hidenori Faculty of Engineering in Kyushu,Kinki University,Professor, 九州工学部, 教授 (50108643)
OHYA Masanori Faculty of Science and Technology,Science University of Tokyo,Professor, 理工学部, 教授 (90112896)
SAITO Kichisuke Faculty of Science,Niigata University,Professor, 理学部, 教授 (30018949)
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| Research Abstract |
Details of results (including names of contributors) should be found in "THE RESEARCH REPORT"; We will state only the research objects with which each research group has mainly concerned through the project.
(1)(Research group on operator algebras and function algebras) Index theory for II_1 factors, completely positive maps, non-abelian dynamical systems, Kac groups and quantum groups (Operator algebra theory), and Douglas algebras, Bourgain algebras, Toeplitz and Hankel operators, etc. (Function algebra theory), are investigated in this group; many results which seem to be important arer given.
(2)(Research group on Banach function spaces) Non-commutative processes (stability of their system), Clarkson type inequality, (linear, semi-linear, and non-linear) evolution equation, entropies of quantum systems (with applications to heredity theory), non-linear Perron-Frobenius theory, outer functions, etc., are investigated from various stand points and many results are obtained.
(3)(Research
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group on representation theory) Representations of quantum groups, infinite-dimensional Lie groups, and Lie algebras and their representations, Kostant theory and Feynman path integral, homogeneous spaces of semi-simple Lie groups, etc., were investigated extensively.
(4)(Research group on partial differential equations) Semigroups of operators and evolution equation, asymptotic behavior of interfaces and blow-up of solutions for non-linear equations, Scattering theory for Schrodinger operators, mathematical study of quantum field theory, WKB method,microlocal analysis, Torotter type formulas, etc., were studied and added greately to our knowledge of the theory.
(5)(Research group on real analysis) Studies on global density theorem for Federer measures, Sato's generalized functions valued in locally convex spaces, Fefferman-Phong inequality, quasi-invariant measures for commutative transformation groups, extrapotation for infinite measure spaces, etc., are aimed and results which seem to be influential are obtained. Less
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