Boundary behavior of anlytic functions and harmonic functions

解析函数和调和函数的边界行为

基本信息

批准号：
09640230
负责人：
SEGAWA Shigeo
金额：
$ 1.15万
依托单位：
Daido Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

项目摘要

(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.

(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.他们还表征了R的最小Martin边界点的数量，该点位于R的最小Martin边界点上，就精细的拓扑而言。他们表明，对于R Green功能的R应用这些结果，他们表明，R上的每个正谐波功能都是预测对R的正谐波功能的回调，并且仅当每个最小的Martin边界点P的每个最小的Martin边界点P r的最小Martin r边界点的数量是P，p的最小Martin边界点是一个。 Schrodinger方程在r^n上具有给定签名的度量电位，他们表明，如果D是连续的域并且在D上存在Green的功能，则有一个包含D的域F，并且存在Green的功能。（3）Ueda扩展了Nevanlinna的结果，Nevanlinna对三个Meromoromormormormormormormorphic函数及其Zero-One-One-One-One-One-One-One-One-One-One-One-One-One-One-One-Ono-One-One-One-One-One-One-One-One-One-One-Poles集。他还表明，从某种意义上说，一定的零子形态函数的零一孔集很薄。（4）纳里塔表明，如果在开放的riemaun表面上具有分析函数的代数a将Riemaun表面r的分析函数分开，则将某个较小的R的点分开，那么R.More的点弱分离，他构建了两个示例，他会构建两个示例，显示出结果的范围是锋利的。