| Project/Area Number |
12640147
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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 | HOKKAIDO UNIVERSITY |
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Principal Investigator |
HAYASHI Mikihiro Hokkaido, Univ., Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (40007828)
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| Co-Investigator(Kenkyū-buntansha) |
NAGASAKA Yukio Hokkaido, Univ., College of Medical Technology, Prof., 医療技術短期大学部, 教授 (50001855)
TACHIZAWA Kazuya Hokkaido, Univ., Grad. School of Sci., Asso. Prof., 大学院・理学研究科, 助教授 (80227090)
NAKAZI Takahiko Hokkaido, Univ., Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (30002174)
JIMBO Toshiya Nara Univ. of Education, Fac. Of Educ., Prof., 教育学部, 教授 (80015560)
IZUCHI Keiji Niigata Univ., Fac. Of Sci., Prof., 理学部, 教授 (80120963)
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| Project Period (FY) |
2000 – 2002
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| Keywords | Rieman surface / bounded analytic function / maximal ideal space / point separation problem / isomorphic problem / Hardy class / Myrberg phenomena / uniqueness theorem |
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| Research Abstract |
The algebra of all bounded analytic functions on a Riemann surface is of course determined by the Riemann surface. This converse is no longer obvious, and we call it the isomorphic problem. If a Riemann surface admits a meromorphic function bounded at the boundary of the surface and if bounded analytic functions separate the points of the surface, then the answer is yes. However, the investigator found a counter example when a surface admits no such meromorphic function.
When we ask the isomorphic problem, we assume that bounded analytic functions (weakly) separate the points of a surface, for otherwise isomorphic problem fails always. Thus, it is an interesting problem to determine whether a given surface is separating or not with respect to bounded analytic functions. This problem is also hard to solve in general. The investigator, together with Prof. Mitsuru Nakai and Dc. Yasuyuki Kobayashi, consider the case of a two-sheeted disc, where the projection of the sequence of ramification points converging to the center of the disc. We considered the case that a sequence of small discs centered at ramification points are removed, and found several sufficient conditions for separating and also not separating.
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