Characterizations of Some Domains via Carathéodory Extremals
Characterizations of Some Domains via Carathéodory Extremals
In this paper we characterize the unit disc, the bidisc and the symmetrized bidisc $$\begin{aligned} G =\{(z+w,zw):|z|<1,\ |w|<1\} \end{aligned}$$in terms of the possession of small classes of analytic maps into the unit disc that suffice to solve all Carathéodory extremal problems in the domain.