The Eremenko-Lyubich class B consists of transcendental entire functions with bounded singular set and the Speiser class S ⊂ B is made up of functions with a finite singular set. In [4] I gave a method for constructing Eremenko-Lyubich functions that approximate certain simpler functions called models. In this paper, I show that all models can be approximated in a weaker sense by Speiser class functions, and that the stronger approximation of [4] can fail for the Speiser class. In particular, I… CONTINUE READING

Lectures on quasiconformal mappings, volume 38 of University Lecture Series. American Mathematical Society, Providence, RI, second edition, 2006. With supplemental chapters by C