2001 Fiscal Year Final Research Report Summary
Research on ideal boundaries of open Riemann surfaces
| Project/Area Number |
12640192
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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 Daido Institute of Technology, Engineering, 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) |
2000 – 2001
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| Keywords | Picard principle / essential set / Royden compactification / Schrodinger operator / Martin boundary / meromorphic function / interpolating sequence / harmonic dimension |
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| Research Abstract |
Martin ideal boundaries. Tada and Nakai showed that the magnitude of an essential set of a density can be prescribed in advance to a certain extent if the Picard principle is valid for the density. Imai proved that the Picard dimension of a signed measure of quasi Kato class is positive if and only if a quadratic form induced by a Schrodinger operator with the measure of its potential is positive definite. Royden ideal boundaries. Nakai and Tada proved the existence of two Riemannian manifolds or even two Euclidean domains such that these two domains are homeomorphic, their two Royden algebras are ring isomorphic, their two Royden compactifications are homeomorphic, and yet they are not almost quasiconformally equivalent. Boundary behabior of harmonic functions. Segawa constructed a covering surface D and a projection (ψ of the unit disk D satisfying HB(D)oψ= HB(D) and HP(D)oψ≠HP(D). Segawa completely determined the topological structure of the Martin boundaries of 3-sheeted covering surfaces of Heins type including minimal boundaries. Nakai constructed an infinitely sheeted covering surface of the complex plane which is a Heins surface such that the harmonic dimension of it is the cardinal number of the continuum. Value distribution theory of meromorphic functions. Ueda solved the Problem 2.27 in Hayman's book in a special case. Ueda proved an improvement of Gundersen's 2-2 theorem by Muess. Point separation by bounded analytic functions and theory of function algebra. Narita gave a sufficient condition for existence of harmonic interpolating but not interpolating sequence in a plane region. Narita considered a sequence in a plane region such that the infimum of the diameter of the complement of the region is positive and divided the sequence into two sequences. He showed that the sequence is an interpolating sequence if the closure of two divided sequences are disjoint in the maximal ideal space.
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Research Products
(28 results)
