Research on ideal boundaries of open Riemann surfaces

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 I D12西耶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&lt；p&lt；d of the Riemannian manifolds of the same dimension d[less than or equal]2a…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：Less

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