2006 Fiscal Year Final Research Report Summary
Research on ideal boundaries of open Riemann surfaces
| Project/Area Number |
17540178
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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 |
TADA Toshimasa Daido Institute of Technology, Liberal Arts and Sciences, Professor, 教養部, 教授 (90105635)
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| Co-Investigator(Kenkyū-buntansha) |
SEGAWA Shigeo Daido Institute of Technology, Liberal Arts and Sciences, Professor, 教養部, 教授 (80105634)
UEDA Hideharu Daido Institute of Technology, Liberal Arts and Sciences, Professor, 教養部, 教授 (20139968)
NARITA Junichirou Daido Institute of Technology, Liberal Arts and Sciences, Professor, 教養部, 教授 (30189211)
FUTAMURA Toshiide Daido Institute of Technology, Liberal Arts and Sciences, Associate Professor, 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) |
2005 – 2006
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| Keywords | Picard dimension / basic perturbation / capacity inequality / type problem for covering surfaces / bounden harmonic functions / Lebesgue space with variable exponents / unicity theorem for meromorphic functions / interpolating sequence |
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| Research Abstract |
Martin ideal boundaries. Nakai and Tada showed that that the Picard dimensions of hyperbolic radial Radon measures are invariant under basic perturbations. Nakai and Tada showed the growth invariance of the hyperbolicity for hyperbolic signed Kato measures and the contraction invariance of the hyperbolicity for hyperbolic signed Holder measures. Imai gave a condition for signed kato measures to be non elliptic type. Royden ideal boundaries. Nakai studied on capacities considered in the complex sphere and a covering surface obtained by pasting the complex sphere with its copy crosswise along a pasting arc. He established the capacity inequality. He also derived a variational formula for the capacity and showed that the capacity changes smoothly as one branch point of the arc moves in the subsurface. Boundary behavior of harmonic functions. Segawa proved that there exists no unbounded positive harmonic functions on hyperbolic Riemann surface if and only if the minimal Martin boundary of the surface consists of finitely many points with positive harmonic measure. Nakai and Segawa gave sufficient conditions for a covering surface obtained by pasting the complex sphere with its copies crosswise along a pasting arcs to equivalent with the complex plane. Futamura characterized ranges of bounded maximal operators of Lebesgue spaces with variable exponents. Value distribution theory of meromorphic functions. Ueda gave that two unicity theorems for nonconstant meromorphic functions in the whole complex plane that share one set and two values in some sense. Point separation by bounded analytic functions and theory of function algebra. Narita described two sufficient conditions when harmonic interpolating sequences do not coincide. He also gave an example of domain and a sequence, which is a harmonic interpolating sequence, but not an interpolating sequence.
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