Convergence of Sequences of Linear Fractional Transformations and of Continued Fractions

Abstract

Recently Piranian and Thron [3] gave a classification of the convergence behavior of sequences of linear fractional transformations. They were interested in part in providing tools which might be helpful in deriving results for continued fractions. No such applications have as yet been forthcoming. In this article we consider the classification problem for a more restricted set of sequences, namely those that map the unit circular disk into itself.