2000 Fiscal Year Final Research Report Summary
Structure of polynomial hulls of graphs on the torus or sphere in C^n and polynomial approximation
| Project/Area Number |
11640167
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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 |
Basic analysis
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| Research Institution | Nara University of Educaiton |
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Principal Investigator |
JIMBO Toshiya Nara Univ. of Education., Facul. of Educ., Dpt. of Math, Prof., 教育学部, 教授 (80015560)
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| Co-Investigator(Kenkyū-buntansha) |
MINAMI Haruo Nara Univ. of Education., Facul. of Educ., Dpt. of Math, Prof., 教育学部, 教授 (90047233)
ADACHI Kenzo Nagasaki University, Facul. of Educ., Dpt. of Math., Prof., 教育学部, 教授 (70007764)
SAKAI Akira Osaka Prefecture Univ., Facul. of Engi., Dept. of Math., Emer. Prof., 工学部, (名誉教授) (70029627)
KAWASAKI Ken-ichiroh Nara Univ. of Educ., Facul. of Educ., Dpt. of Math, Asso. Prof, 教育学部, 助教授 (60288040)
KAWAKAMI Satoshi Nara Univ. of Education., Facul. of Educ., Dpt. of Math, Prof., 教育学部, 教授 (20161284)
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| Project Period (FY) |
1999 – 2000
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| Keywords | polynomial hull / polynomial approximation / continuation of holomorphic functions / function algebra / framed manifold / hypergroup / local cohomology |
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| Research Abstract |
For the problem to determine a polynomial hull, it is important to find the method how to cutt off the surplus part from a certain set which contains the polynomial hull. When the defining function of a graph on the unit torus in C^2 has an extension in antiholomorphic functions on the unit bidisk, we considered a lemma obtained by combining Rossi's local maximum modulus principle with the properties of totally real manifolds to the problem. By the lemma we determined that the polynomial hull of the graph on the torus of a function which is the complex conjugate of a homogeneous polynomial. We can apply the method to the problem in the case of the sphere.
Adachi proved that if V is a regular subvariety of non-degenerate analytic polyhedron Ω in C^n and V intersects transversally in a certain sense, then each function in H^p(V) has an extention in H^p(Ω). Minami consider the problem whethter a compact Lie group is framed cobordant to the boundary of a parallelizable manifold or not. And he proved that a comjecture by Becker and Schultz on the 3-components of classical Lie groups is true. Kawasaki showed that if A is a Cohen-Macaulay local ring of dimension d, the Lyubezuniku number of A is always one. For an action of a finite group on a finite commutative hyper-group, Kawakami succeeded to give a construction of a character hypergroup associated which the semi-direct product hypergroup.
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