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arXiv · 1802.09067

Characterizations of some domains via Carath\'eodory extremals

J. Agler·Z. A. Lykova·N. J. Young
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Abstract

In this paper we characterize the unit disc, the bidisc and the symmetrized bidisc \[ G =\{(z+w,zw):|z|<1,\ |w|<1\} \] in terms of the possession of small classes of analytic maps into the unit disc that suffice to solve all Carath\'eodory extremal problems in the domain.

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J. Agler, Z. A. Lykova, N. J. Young. 2018-02-25. Characterizations of some domains via Carath\'eodory extremals. https://arxiv.org/abs/1802.09067

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