| Project/Area Number |
16540175
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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 | Daido Institute of Technology |
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Principal Investigator |
SEGAWA Shigeo Daido Institute of Technology, School of General Arts and Science, Professor, 教養部, 教授 (80105634)
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| Co-Investigator(Kenkyū-buntansha) |
TADA Toshimasa Daido Institute of Technology, School of General Arts and Science, Professor, 教養部, 教授 (90105635)
UEDA Hideharu Daido Institute of Technology, School of General Arts and Science, Professor, 教養部, 教授 (20139968)
NARITA Junichiro Daido Institute of Technology, School of General Arts and Science, Professor, 教養部, 教授 (30189211)
FUTAMURA Toshihide Daido Institute of Technology, School of General Arts and Science, Lecturer, 教養部, 講師 (90387605)
NAKAI Mitsuru Nagoya Institute of Technology, Professor Emeritus, 名誉教授 (10022550)
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| Project Period (FY) |
2004 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 2005: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2004: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | type problem for covering surfaces / Martin Boundary / quasiconformal mapping / harmonic dimension / Picard principle / negligible pertubation / bounded holomorphic functions / interpolating sequences / 放物型 / 定常シュレディンガー方程式 / グリーン関数 / 峰集合 / リーマン面の型問題 / 有界正則関数環 |
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| Research Abstract |
1.Riemann surfaces
(1)A sufficient condition was given for certain infinitely sheeted covering surfaces of the complex plane in order to possess no Green's functions.
(2)For hyperbolic (i.e.possessing Green's function) Riemann surfaces R, it was shown that there exists no unbounded positive harmonic functions on R if and only if the Martin boundary of R consists of finitely many minimal points and each minimal point has positive harmonic measure. Moreover, for hyperbolic Riemann surfaces R, it was shown that there exists no Dirichlet infinite positive harmonic functions on R if and only if the Martin boundary of R consists of finitely many minimal points, each minimal point has positive harmonic measure and each minimal function is Dirichlet finite.
(3)It was shown that, if 2 or 3-shetted unlimited covering surfaces R and S of the complex plane are quasiconformal equivalent to each other, then the harmonic dimension of R is equal to that of S.
2.Picard Principle
(1)It was shown that the Picard dimension of a rotation free hyperbolic signed Radon measure dm is equal to that of a measure obtained by adding a fundamental measure to dm.
(2)For Green's function with respect to a staionary invariant Schoredinger equation with a Radon measure as potential, generalizations of Ohtsuka's theorem, Herve's theorem and Lahtinen' theorem are given.
3.Bounded holomorphic functions
(1)It was shown that a sequence in a plane domain satisfying a certain geometric condition is interpolating if the closures of two parts of the sequence is mutually disjoint.
(2)It was shown that if the fiber of the maximal ideal space over a regular boundary point of a plane domain is not a peak set, then there exists a sequence converging to the boundary point which is not interpolating but harmonic interpolating.
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