Research on ideal boundaries of open Riemann surfaces

开黎曼曲面理想边界的研究

• 批准号: 17540178
• 负责人: TADA Toshimasa
• 金额: $ 1.47万
• 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: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-17540178/
• 关键词: 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; 定常シュレーディンガー方程式

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.

马丁理想边界。 Nakai和Tada表明，在基本扰动下，双曲线径向rad测量的PICARD尺寸是不变的。 Nakai和Tada显示了双曲线签名的Kato测量值的双曲线的生长不变性以及双曲线签名持有人测量的双曲线的收缩不变性。 IMAI给出了签名的Kato措施是非椭圆类型的条件。罗伊登理想边界。 Nakai研究了复杂球中考虑的能力和通过沿粘贴弧沿副本沿副本粘贴副本粘贴的覆盖表面。他确立了能力不平等。他还得出了容量的变异公式，并表明当弧的一个分支点在地下移动时，容量会平稳变化。谐波功能的边界行为。 Segawa证明，当且仅当表面的最小Martin边界由有限的许多点组成，具有正谐波测量的有限点时，没有双曲线riemann表面上的无限正谐波函数。 Nakai和Segawa通过沿粘贴弧沿横向副本将复合物粘贴到与复杂平面相等的副本上获得的覆盖面提供了足够的条件。 Futamura表征了具有可变指数的Lebesgue空间的有限最大运营商的范围。子形函数的价值分布理论。 UEDA给出了整个复杂平面中非构型杂形函数的两个Unicity定理，从某种意义上说，它们共享一个集合和两个值。通过有限的分析函数和功能代数理论分离点。当谐波插值序列不重合时，纳里塔描述了两个足够的条件。他还举例说明了域和一个序列，这是一个谐波插值序列，但不是插值序列。

项目成果

Plane domains with harmonic interpolating sequences which are not interpolat-ing sequences

具有非插值序列的谐波插值序列的平面域

• 发表时间: 2005
• 期刊: Kodai Math. J. 28・2
• 作者: Takuya Hosokawa;Shuichi Ohno;Hidenori Fujiwara;藤原 英徳;Hidenori Fujiwara;藤原英徳;Hidenori Fujiwara;H.Fujiwara;Hidenori Fujiwara;Hidenori Fujiwara;Hidenori Fujiwara;Hidenori Fujiwara;藤原 英徳;Hidenori Fujiwara;藤原 英徳;Hidenori Fujiwara;T.Futamura;T.Futamura;T.Futamura;T.Futamura;H.Masaoka;M.Nakai;M.Nakai;M.Nakai;T.Futamura;T.Futamura;T.Futamura;T.Futamura;H.Masaoka;M.Nakai;M.Nakai;M.Nakai;T.Futamura;T.Futamura;T.Futamura;M.Nakai;M.Nakai;T.Futamura;T.Futamura;T.Futamura;T.Futamura;H.Masaoka;M.Nakai;M.Nakai;M.Nakai;中井三留;J.Narita
• 通讯作者: J.Narita

Harmonic Liouville Theorem for Exterior Domains Revisited

重温外部域的调和刘维尔定理

• 发表时间: 2005
• 期刊: Far East J. Math. Sci. 18・1
• 作者: Takuya Hosokawa;Shuichi Ohno;Hidenori Fujiwara;藤原 英徳;Hidenori Fujiwara;藤原英徳;Hidenori Fujiwara;H.Fujiwara;Hidenori Fujiwara;Hidenori Fujiwara;Hidenori Fujiwara;Hidenori Fujiwara;藤原 英徳;Hidenori Fujiwara;藤原 英徳;Hidenori Fujiwara;T.Futamura;T.Futamura;T.Futamura;T.Futamura;H.Masaoka;M.Nakai;M.Nakai;M.Nakai;T.Futamura;T.Futamura;T.Futamura;T.Futamura;H.Masaoka;M.Nakai;M.Nakai;M.Nakai;T.Futamura;T.Futamura;T.Futamura;M.Nakai;M.Nakai;T.Futamura;T.Futamura;T.Futamura;T.Futamura;H.Masaoka;M.Nakai;M.Nakai
• 通讯作者: M.Nakai

Harmonic Liouville Theorem for Exterior Do- mains Revisited

重温外域调和刘维尔定理

• 发表时间: 2005
• 期刊: Far East J.Math.Sci. vol.18-1
• 作者: Takuya Hosokawa;Shuichi Ohno;Hidenori Fujiwara;藤原 英徳;Hidenori Fujiwara;藤原英徳;Hidenori Fujiwara;H.Fujiwara;Hidenori Fujiwara;Hidenori Fujiwara;Hidenori Fujiwara;Hidenori Fujiwara;藤原 英徳;Hidenori Fujiwara;藤原 英徳;Hidenori Fujiwara;T.Futamura;T.Futamura;T.Futamura;T.Futamura;H.Masaoka;M.Nakai;M.Nakai;M.Nakai;T.Futamura;T.Futamura;T.Futamura;T.Futamura;H.Masaoka;M.Nakai;M.Nakai;M.Nakai;T.Futamura;T.Futamura;T.Futamura;M.Nakai;M.Nakai;T.Futamura;T.Futamura;T.Futamura;T.Futamura;H.Masaoka;M.Nakai;M.Nakai;M.Nakai;中井三留;J.Narita;H.Ueda;T.Futamura;T.Futamura;T.Futamura;T.Futamura;H.Masaoka;M.Nakai;M.Nakai
• 通讯作者: M.Nakai

The dependance of capacities on moving branch points

容量对移动分支点的依赖性

• 期刊: Nagoya Math. J. (掲載決定)
• 作者: Takuya Hosokawa;Shuichi Ohno;Hidenori Fujiwara;藤原 英徳;Hidenori Fujiwara;藤原英徳;Hidenori Fujiwara;H.Fujiwara;Hidenori Fujiwara;Hidenori Fujiwara;Hidenori Fujiwara;Hidenori Fujiwara;藤原 英徳;Hidenori Fujiwara;藤原 英徳;Hidenori Fujiwara;T.Futamura;T.Futamura;T.Futamura;T.Futamura;H.Masaoka;M.Nakai;M.Nakai;M.Nakai;T.Futamura;T.Futamura;T.Futamura;T.Futamura;H.Masaoka;M.Nakai;M.Nakai;M.Nakai;T.Futamura;T.Futamura;T.Futamura;M.Nakai;M.Nakai;T.Futamura;T.Futamura;T.Futamura;T.Futamura;H.Masaoka;M.Nakai;M.Nakai;M.Nakai;中井三留;J.Narita;H.Ueda;T.Futamura;T.Futamura;T.Futamura;T.Futamura;H.Masaoka;M.Nakai;M.Nakai;M.Nakai;M.Nakai;J.Narita;H.Ueda;M.Nakai;M.Nakai;M.Nakai;M.Nakai;中井三留;H.Masaoka;H.Masaoka;H.Ueda;J.Narita;T.Futamura;T.Futamura;T.Futamura;M.Nakai;M.Nakai;M.Nakai
• 通讯作者: M.Nakai

Green functions of Schrodinger operators

薛定谔算子的绿色函数

• 发表时间: 2005
• 期刊: Bull.Daido Inst.Tech. vol.41
• 作者: Takuya Hosokawa;Shuichi Ohno;Hidenori Fujiwara;藤原 英徳;Hidenori Fujiwara;藤原英徳;Hidenori Fujiwara;H.Fujiwara;Hidenori Fujiwara;Hidenori Fujiwara;Hidenori Fujiwara;Hidenori Fujiwara;藤原 英徳;Hidenori Fujiwara;藤原 英徳;Hidenori Fujiwara;T.Futamura;T.Futamura;T.Futamura;T.Futamura;H.Masaoka;M.Nakai;M.Nakai;M.Nakai;T.Futamura;T.Futamura;T.Futamura;T.Futamura;H.Masaoka;M.Nakai;M.Nakai;M.Nakai;T.Futamura;T.Futamura;T.Futamura;M.Nakai;M.Nakai;T.Futamura;T.Futamura;T.Futamura;T.Futamura;H.Masaoka;M.Nakai;M.Nakai;M.Nakai;中井三留;J.Narita;H.Ueda;T.Futamura;T.Futamura;T.Futamura;T.Futamura;H.Masaoka;M.Nakai;M.Nakai;M.Nakai;M.Nakai
• 通讯作者: M.Nakai