1999 Fiscal Year Final Research Report Summary
Research on ideal boundaries of open Riemann surfaces
| Project/Area Number |
10640190
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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, Engineering, Professor, 工学部, 教授 (90105635)
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| Co-Investigator(Kenkyū-buntansha) |
UEDA Hideharu Daido Institute of Technology, Engineering, Professor, 工学部, 教授 (20139968)
SEGAWA Shigeo Daido Institute of Technology, Engineering, Professor, 工学部, 教授 (80105634)
IMAI Hideo Daido Institute of Technology, Engineering, Professor, 工学部, 教授 (00075855)
NAKAI Mitsuru Nagoya Institute of Technology, Professor emeritus, 名誉教授 (10022550)
NARITA Junichirou Daido Institute of Technology, Engineering, Assistant Professor, 工学部, 助教授 (30189211)
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| Project Period (FY) |
1998 – 1999
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| Keywords | Picard Dimension / Picard principle / Maretin ideal boundary / Royden compactification / bounded harmonic function / meromorphic function / Myrberg phenomenon / interpolating sequence |
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| Research Abstract |
Martin ideal boundaries. Imai showed that if the Picard dimension of a stationary Schrodinger operator with a signed Radon measure of quasi Kato class as its Potential is positive then it is essentially selfadjoint on the LィイD12ィエD1 space of the Lebesgue measure and the total variation of the measure. Tada and Nakai obtained behavior of boundary values from boundary behavior of Dirichlet solutions of stationary Schrodinger equations. Tada and Nakai determined the maximal growth of a rotation free density which is an exceptional perturbation for Picard principle. Segawa determined the Martin boundaries of m-sheeted cyclic unlimited covering surfaces with the punctured Riemann sphere as its base surfaces. Royden ideal boundaries. Nakai proved that any quasibounded harmonic function on any continuous domain can be expressed as solution of Dirichlet problem. Nakai showed that Royden p-compactifications for 1 < p < d of the Riemannian manifolds of the same dimension d【less than or equal】2 a
… More
re homeomorphic if and only if there exists a almost quasiisometric homeomorphism between these Riemannian manifolds. Boundary behavior of harmonic functions. Sego gave a necessary and sufficient condition for the spaces of positive harmonic functions on a p-sheeted unlimited Riemann surface and its base surface being same. Tada and Nakai proved the extended Liouville theorem for a class of functions which properly contains polyharmonic functions. Value distribution theory of meromorphic functions. Ueda studies on rarity of 0 - 1 - pole set of nonconstant meromorphic functions on the complex plane. Point separation by bounded analytic functions and theory of function algebra. Nakai showed that the uniqueness theorem is sufficient but not necessary for the occurrence of the Myrberg phenomenon. Narita showed some necessary and sufficient condition for week separation by an algebra of analytic functions Narita showed some sufficient condition for an interpolating sequence in a bounded domain being a harmonic interpolating sequence. Less
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Research Products
(34 results)
