Research on ideal boundaries of open Riemann surfaces

开黎曼曲面理想边界的研究

基本信息

批准号：
10640190
负责人：
TADA Toshimasa
金额：
$ 1.09万
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：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

项目摘要

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

马丁理想边界。 IMAI表明，如果固定的Schrodinger操作员的PICARD尺寸具有符号ra的ra尺测量值，则对Quasi Kato类的测量为正面，因为其潜力是正的，那么它实际上是Lebesgue测量的LII D12 D1空间上的自我偶像，并且测量的总变化。 TADA和NAKAI从固定Schrodinger方程的Dirichlet解的边界行为中获得了边界值的行为。 TADA和NAKAI确定了自由密度的最大生长，这是PICARD原理的特殊扰动。塞加瓦（Segawa）确定了M的Martin Cyclic Unlimited覆盖表面的Martin边界，并用刺穿的Riemann Sphere作为其基本表面。罗伊登理想边界。 Nakai证明，任何连续域上的任何准谐波功能都可以表示为Dirichlet问题的解决方案。纳凯（Nakai）表明，相同尺寸的riemannian歧管的1 <p <d小于或相等的】2a的Royden p- compactification在这些riemannian歧管之间几乎几乎存在准同型同构时，只有在几乎存在准静脉均衡时，就会更加同构时。谐波功能的边界行为。 SEGO为p片无限riemann表面上的正谐波函数的空间提供了必要和充分的条件，其基本表面相同。 Tada和Nakai证明了适当包含多结功能的一类功能的扩展Liouville定理。子形函数的价值分布理论。 UEDA对稀有性的稀有性研究在复杂平面上的非晶体杂形函数的杆子集。通过有限的分析函数和功能代数理论分离点。 Nakai表明，唯一性定理足够，但对于Myrberg现象的发生并不必需。纳里塔（Narita）通过分析函数代数纳里塔（Narita）的代数表现出一些必要且充分的条件，在有界结构域中的插值序列是谐波插值序列的一定条件。较少的