| Project/Area Number |
11304009
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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 | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Tokyo Woman's Christian University |
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Principal Investigator |
MIYACHI Akihiko Tokyo Woman's Christian University, College of Arts and Sciences : Professor, 文理学部, 教授 (60107696)
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| Co-Investigator(Kenkyū-buntansha) |
WAKAYAMA Masato Kyushu University, Department of Mathematical Sciences, Professor, 大学院・数理学研究科, 教授 (40201149)
CHO Muneo Kanagawa Industrial University, Faculty of Engineering, Professor, 工学部, 教授 (10091620)
KOBAYASI Kazuo Waseda University, Faculty of Education, Professor, 教育学部, 教授 (30139589)
OHYA Masanori Science University of Tokyo, Faculty of Science and Engineering, Professor, 理工学部, 教授 (90112896)
OKAJI Takashi Kyoto University, Department of Science : Associate Professor, 大学院・理学研究科, 助教授 (20160426)
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| Project Period (FY) |
1999 – 2000
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| Keywords | Singular integral / Hardy space / Navier-Stokes equation / Phase transition / Dirac equation / Pfaffian / p-hyponormal operator / chaos theory |
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| Research Abstract |
The research is extended to the following 5 areas : (1) Harmonic analysis by real variable methods ; (2) Partial differential equations by functional- analysis method ; (3) Operator algebras and function algebras ; (4) Represen- tation theory ; (5) Quantum logics and function spaces.
Our main results are the following. In the area (1) : we obtained real variable characterization for the weighted Hardy spaces on a domain and for the Herz-type Hardy spaces ; proved boundedness of several singular integral operators with nonregular kernels ; and got Hardy space estimate for the mul- tilinear operator which is defined as a sum of products of singular integrals. In (2) : we got strong unique continuation theorem for the Maxwell equation, the Dirac equation, and for the Schrodinger equations ; studied propagation of singularities for the Schrodinger equations ; used Hardy space estimate to study the Stokes operator ; proved time-global existence of solutions to the Cauchy problem for the Navier-Stokes equation with nondecaying initial data ; studied the properties of the attractor of the nonlinear dynamical systoms related to the phase-transition phenomena ; obtained several algorithms for computing the Grothendieck residues, de Rham cohomology of algebraic varieties, and D-modules. In (3) : we gave a generalization of Putnam's inequality ; got the classification of actions of factors to operator algebras ; constructed the index theory for C^* algebras ; and solved the single generator problem on the Bohr group. In (4) : we got Hardy space theory on rank 1 semisimple Lie group ; and got summation formula for Pfaffians and its applications. In (5) : we gave a solution to an NP complete problem as an application of the quantum algorithm and the chaos theory ; studied several properties of p-hyponormal operators.
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