Project/Area Number  07640242 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
解析学

Research Institution  Nippon Institute of Technology 
Principal Investigator 
OHNO Shuichi Nippon Institute of Technology, Department of Technology, Associate Professor, 工学部, 助教授 (20265367)

CoInvestigator(Kenkyūbuntansha) 
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)

Project Fiscal Year 
1995 – 1996

Project Status 
Completed(Fiscal Year 1996)

Budget Amount *help 
¥2,200,000 (Direct Cost : ¥2,200,000)
Fiscal Year 1996 : ¥900,000 (Direct Cost : ¥900,000)
Fiscal Year 1995 : ¥1,300,000 (Direct Cost : ¥1,300,000)

Keywords  Hardy Space / Tociplitz Operator / Composition Operator / Manifold / Grassmann Geometry / Sphere / Differential Equation / Entire Function / Hardy空間 / Hankel作用素 / 合成作用素 / 純虚ケーリー代数 / 剛性定理 / 6次元球面 / 微分方程式 / 複素力学系 / angular derivative / 多様体 / グラスマン幾何 / Bergman空間 / Hapf超曲面 / リーマン面 / 整関数 
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 5dimensional submanifolds of a nearly Kaehler 6spherc in the purcly imaginary octonians. Main result is that for any hypersurface of 6sphere, there exists a grobal quaternion structure on the contact distribution. Moreover he studied tublar hypersurfaces. He iedentified the symplectic group SP (1) with the 3dimensional sphere and considered parametrized 3dimcnsional submanifolds in terms of SP (1) orbits in the 6sphere. (3) Hashimoto investig
… More
ated submanifolds theory in a 6dimensional sphere S^6. A 6dimensional sphere has an almost Hermitian structure.It was proved that ndimensional 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 2dimensional submanifolds of a 6dimensional sphere is called the Jholomorphic 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 Jholomorphic 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
