Category Results for Tsuji Functions

Abstract

Let D be the unit disk, |z| < 1, and H(D) the Fréchet space of holomorphic functions on D, provided with the topology of uniform convergence on compact subsets of D. If f is meromorphic in D, we denote by

Boundary characteristics of meromorphic functions with summable spherical derivation and annular functions. Consideration

“…Если через Z(f) обозначим множество нулей аннуларной функции f, известно что Z(f) бесконечное множество точек в D. Пусть Z'(f) -множество предельных точек Z(f). Тогда Дальнейшие интересные иследования функциональных свойств аннуларных функций можно найти, например, в [41][42][43][44][45][46].…”

Strongly Annular Tsuji Functions

“…To facilitate the discussion of the spherical image of the arc y r *, we denote by \j/ the stereographic projection of the plane onto the Riemann sphere. If the arc Sbilr*) begins at the inner boundary of the «th dirty annulus, then the behaviour of the function \p of og b on the initial part of y r * is determined almost entirely by the nth term in (1), and therefore the spherical image of the initial part of y r * consists of smooth loops around the north pole, of approximate diameter 2e/a n . As g b (y r *) penetrates deeper into the dirty annulus, the (« + l)st term in (1) affects the curve \\i of og b (y r *) by generating shallow waves of high frequency.…”