Research on ideal boundaries of open Riemann surfaces

马丁的理想界限。Nakai和Tada证明了双曲径向Radon测度的Picard维数在基本扰动下是不变的。Nakai和Tada证明了双曲符号Kato测度的双曲性的增长不变性和双曲符号Holder测度的双曲性的收缩不变性。Imai给出了带符号Kato测度为非椭圆型的一个条件。罗伊登理想的边界。Nakai研究了复数球面和复数球面沿粘贴弧线横向粘贴所得到的复盖面的容量。他确立了能力不平等。他还推导了容量的变分公式，并证明了当弧线的一个分支点在地下移动时，容量变化是平稳的。调和函数的边界性质。Segawa证明了双曲Riemann曲面上不存在无界正调和函数当且仅当该曲面的极小Martin边界由有限多个具有正调和测度的点组成。Nakai和Segawa给出了复球面沿粘贴圆弧横向粘贴其副本与复平面等价的覆盖曲面的充分条件。Futamura刻画了具有可变指数的勒贝格空间的有界极大算子的值域。亚纯函数的值分布理论。Ueda给出了全复平面上具有一个或两个公共值的非常数亚纯函数的两个唯一性定理。有界解析函数的点分离与函数代数理论。Narita给出了调和插值序列不重合的两个充分条件。他还给出了一个域和一个序列的例子，它是调和插值序列，但不是插值序列。

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.