1996 Fiscal Year Final Research Report Summary
Studies of The Spaces of Analytic Functions and Their Operators
| Project/Area Number |
07640242
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
解析学
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| Research Institution | Nippon Institute of Technology |
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Principal Investigator |
OHNO Shuichi Nippon Institute of Technology, Department of Technology, Associate Professor, 工学部, 助教授 (20265367)
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| Co-Investigator(Kenkyū-buntansha) |
ISHIZAKI Katsuya Nippon Institute of Technology, Department of Technology, Lecturer, 工学部, 講師 (60202991)
HASHIMOTO Hideya Nippon Institute of Technology, Department of Technology, Associate Professor, 工学部, 助教授 (60218419)
FUNABASHI Shoichi Nippon Institute of Technology, Department of Technology, Professor, 工学部, 教授 (40072136)
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| Project Period (FY) |
1995 – 1996
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| Keywords | Hardy Space / Tociplitz Operator / Composition Operator / Manifold / Grassmann Geometry / Sphere / Differential Equation / Entire Function |
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| Research Abstract |
(1) In 1995, Ohno investigated Toeplitz and Hankel operators on harmonic Borgman spaces on the unit disk. Main results are to characterize algebraic properties, boundedness and compactness. There exists a relation between the compactness of Hankel operators and Bourgain algebras. This is a very interesting problem. In 1996, he studied the conditions that differences of two composition operators are compact. He obtained some examples and a necessary condition closely related to the compactness of one composition operator.
(2) Funabashi studied 5-dimensional submanifolds of a nearly Kaehler 6-spherc in the purcly imaginary octonians. Main result is that for any hypersurface of 6-sphere, there exists a grobal quaternion structure on the contact distribution. Moreover he studied tublar hypersurfaces. He iedentified the symplectic group SP (1) with the 3-dimensional sphere and considered parametrized 3-dimcnsional submanifolds in terms of SP (1) -orbits in the 6-sphere.
(3) Hashimoto investig
… More
ated submanifolds theory in a 6-dimensional sphere S^6. A 6-dimensional sphere has an almost Hermitian structure.It was proved that n-dimensional sphere admit almost complex structures except for n*2,6. Also the automorphism group of this almost Hcrmitian structure of S^6 coincide with the exceptional Lie group G_2. The 2-dimensional submanifolds of a 6-dimensional sphere is called the J-holomorphic curves of S^6 if its tangent space is invariant under the almost complex structure. I obtained some classification theorems and a rigidity theorem with respect to the Lie group G_2 about J-holomorphic curves of S^6.
(4) Ishizaki has studied the complex differential equations, mainly admissible solutions of first order algebraic differential equations and complex oscillation for an equation of the form f"+A (z) f=0. Complex dynamics theory has been also of our great interest. Study of hypertranscendency has treated from the two points of view, say complex differential theory and complex dynamics theory. Less
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