Project/Area Number  09640218 
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) 
ETO Kazufumi Nippon Institute of Technology, Department of Technology, Lecturer, 工学部, 講師 (30271357)
ISHIZAKI Katsuya Nippon Institute of Technology, Department of Technology, Associate Professor, 工学部, 助教授 (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 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥3,100,000 (Direct Cost : ¥3,100,000)
Fiscal Year 1998 : ¥1,300,000 (Direct Cost : ¥1,300,000)
Fiscal Year 1997 : ¥1,800,000 (Direct Cost : ¥1,800,000)

Keywords  Hardy Space / Composition Operator / Hopf hypersurface / Cayley algebra / Automorphism group / Meromorphic function / Complex functional equation / Monoid rings / Hardy空間 / 合成作用素 / contact CR構造 / 6次元球面 / 微分方程式 / 超・超越性 / 半群環 / Grobner基底 / 超越函数 / スピノール群 / 値分布論 / 自由分解 
Research Abstract 
(1) Ohno has investigatcd the 1)robleln of components of composition operators on H^* and obtained almost conIl)Iete answers with Professor IL Zhao. We had a talk at Poster Session in International Matlnnaticiazhs Goiigrcss 1998, Berlin, Garmany. After thc talk, wc summarized results to a paper with Profcssor beta.D). MacChicr and(l submitted it. Moreover Olino have studied weighted composition operators on some supnorm function spaces, the disk algebra, H^* and the Bloch space. And R.Zha.o added results in the case of the case little Bloch space. We are ready to submit a manuscript. (2) Funabashmi studied time geometrical properties of the SP(1)orbits which are realized by the special kinds of three actions to tIme nearly Kachler 6sphere. We proved that each orbit is a manifold and somne orbit equips the contact CRstructure having the three distinct principal curvatures. Those results will be contributed in the imear future. We also studied about contact CRsubmanifolds immersed in
… More
Sasakian space forms. Our maun results is that some totally contact Alumbilical contact CRsubmanifold is realized as the 2dimensional torus immersed in the 3dimensional sphere. For those results, we will contribute the paper entitled "On totally contact Alumbilical contact CRsubmanifolds" in collaboration with S.Funabashi, J.H.Kwon and J.S.Pak. (3) Let S^6 be the 6dimensional unit sphere centered at the origin in a 7dimensional Euclidean space. Hashimnoto identified 7dimensional Euchidean space with purely imaginary octon ions ImO (or Cayley algebra). Taking account of algebraic properties of octonions we can define the homogeneous almost Itermitian structure on S^6, We denote by G_2 the Lie group of autornorphisms of O.Then we have S^6 = G_2/SU(3). This almost colnj)lex structure satisfy the nearly Kahler condition. ((*xJ)X = 0) where * is the LeviCivita connection of S^6, and X is any vector field of S^6. We shall give some rigidity theorem of invariant submanifolds up to the action of G_2 amid deterirmine its geometrical invariants. Also, we shall give many examples of 3dimensional CRsnbmanifolds of S^6 explicitely. We obtained some results related to 4dimensional CRsubmanifolds of S^6. (4) Ishmizaki has beemi studying the value distribution theory of meromorphic functions. Applications this theory to com np hex differential equations are of our interest. Algebraic differential equations admitting admissible solutiomis and complex oscillation theory have been comisidered. We are also concerned with functional equations in the complex plane. Results of existence and growth conditions on transcendental meromorphic solutions of Schmrdder's type functional equations, which are some generalizations due to Wittich, are obtained. Moreover, we investigated to lmypertranscendency of merornorphic solutiohs of a certain functional equation. Characterization of the set of meromorphic. functions has been studied from the unicity tlmeoretical poimits of view. (5) Eto investigated homnological properties of monoid rings, especially affine semigroup rings. To do it, lie comistructedI free resolntiomis of them in two cases conibinatorically. They are found in papers "a free resolutions of a binomial ideal" and "finite free resolutions of rnonoid rings". Less
