Research on ideal boundaries of open Riemann surfaces

马丁的理想边界。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保持器测度的双曲性的收缩不变性. Imai给出了带符号Kato测度为非椭圆型测度的一个条件。罗伊登理想边界。中井研究的能力考虑在复杂的领域和覆盖面粘贴复杂的领域与其副本沿沿着一个粘贴弧。他建立了能力不平等。他还推导出一个变分公式的能力，并表明，能力的变化顺利作为一个分支点的弧移动在地下。调和函数的边界行为。Segawa证明了双曲Riemann曲面上不存在无界的正调和函数当且仅当曲面的极小Martin边界由具有正调和测度的100个点组成。Nakai和Segawa给出了复球面与复平面的覆盖曲面等价的充分条件，复球面的复曲面是沿沿着一条贴附弧的复球面。Futamura刻画了变指数Lebesgue空间的有界极大算子的值域。亚纯函数的值分布理论。上田给出了全复平面上分担一个集合和两个值的非常数亚纯函数在某种意义下的两个唯一性定理。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。他还给出了定义域和一个序列的例子，这个序列是调和插值序列，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.