Point separation of a two-sheeted disc by bounded analytic functions (Q1277025)

Let \(\pi:\widetilde\Delta\to\Delta\) be a two-sheeted unlimited covering of \(\Delta\) whose ramification points does not accumulate in \(\Delta\) where \(\Delta\) is the open unit disc. The authors consider the problem when the point of \(\widetilde D=\pi^{-1} (D)\) are separated by bounded analytic functions where \(D\) is a domain of \(\Delta\). They show a sharpness of the non-separating conditions given in [\textit{M. Hayashi}, \textit{M. Nakai} and \textit{S. Segawa}, J. Anal. Math. 61, 293-325 (1993; Zbl 0795.30029)] by improving the separating conditions given there.