Nonuniqueness of Carathéodory extremal functions on the symmetrized bidisc

Jim Agler, Zinaida Lykova, N. J. Young

We survey the Carathéodory extremal problem $\mathrm{Car}\delta$ on the symmetrized bidisc $$G=\{(z+w,zw):|z|<1,|w|<1\}=\{(s,p)\in {\mathbb{C}}^2:|s-\bar{s}p|<1-|p{|}^2\}.$$ W…