1998 Fiscal Year Final Research Report Summary
Boundary behavior of anlytic functions and harmonic functions
| Project/Area Number |
09640230
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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 |
解析学
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| Research Institution | Daido Institute of Technology |
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Principal Investigator |
SEGAWA Shigeo Daido Institute of Technology, Faculty of Engineering, Professor, 工学部, 教授 (80105634)
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| Co-Investigator(Kenkyū-buntansha) |
NAKAI Mitsuru Daido Institute of Technology, Faculty of Engineering, Visiting Professor, 工学部, 客員教授 (10022550)
NARITA Junichiro Daido Institute of Technology, Faculty of Engineering, Assistant Professor, 工学部, 講師 (30189211)
UEDA Hideharu Daido Institute of Technology, Faculty of Engineering, Associate Professor, 工学部, 助教授 (20139968)
TADA Toshimasa Daido Institute of Technology, Faculty of Engineering, Professor, 工学部, 教授 (90105635)
IMAI Hideo Daido Institute of Technology, Faculty of Engineering, Professor, 工学部, 教授 (00075855)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Riemann surface / positive harmonic function / Martin boundary / Schrodinger equation / meromorphic function / unicity thoerem / bounded analytic function / point separation |
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| Research Abstract |
(1) Segawa (with Masaoka (Kyoto Sangyo Univ.)) studied Martin boundary of finitely sheeted unlimited covering surfaces R of a given open Riemann surface R and showed that for a point p of the Martin boundary of R there exists a minimal point p of the Martin boundary of R which lies over p if and only if p is a minimal point. They also characterized the number of minimal Martin boundary points of R which lie over a given minimal Martin boundary point of R, in terms of fine topology. Applying these results, for R with Green's functions, they showed that every positive harmonic function on R is a pullback of a positive harmonic function on R by the projection if and only if for every minimal Martin boundary point p of R the number of minimal Martin boundary points of R which lie over p is one.
(2) Tada and Nakai studied existence or nonexistence of Green's functions on a domain D in the Euclidian space R^n with respect to Schrodinger equation with a given signed measure potential on R^n They showed that if D is a continuous domain and there exist Green's functions on D, then there is a domain F which contains D and on which there exist Green's functions.
(3) Ueda extended a result by Nevanlinna for three meromorphic functions and their zero-one-pole sets. He also showed that the zero-one-pole set of a certain meromorphic function is thin in a sense.
(4) Narita showed that if an algebra A of analytic functions on an open Riemaun surface R separates the points of a certain small subset of R, then A weakly separates the points of R.Moreover, he constructed two examples showing that the result is sharp in a sense.
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Research Products
(36 results)
