Instytut Matematyczny Polskiej Akademii Nauk / pl / Wydawnictwa / Czasopisma IMPAN / Bulletin of the Polish Academy of Sciences. Mathematics / Wszystkie zeszyty

Streszczenie

We study a correspondence $L$ between some classes of functions holomorphic in the unit disc and functions holomorphic in the left halfplane. This correspondence is such that for every $f$ and $w\in\mathbb H$, $\exp(L(f)(w))=f(\exp w)$. In particular, we prove that the famous class $S$ of univalent functions on the unit disc is homeomorphic via $L$ to the class $S({\mathbb H})$ of all univalent functions $g$ on $\mathbb H$ for which $g(w+2\pi i)=g(w)+2\pi i$ and $\lim_{\mathop{\rm Re} z\to-\infty}(g(w)-w)=0$.