Boundary behavior of anlytic functions and harmonic functions

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(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.