Carath\'eodory extremal functions on the symmetrized bidisc
Complex Variables
2018-05-08 v2
Abstract
We show how realization theory can be used to find the solutions of the Carath\'eodory extremal problem on the symmetrized bidisc We show that, generically, solutions are unique up to composition with automorphisms of the disc. We also obtain formulae for large classes of extremal functions for the Carath\'eodory problems for tangents of non-generic types.
Keywords
Cite
@article{arxiv.1712.00749,
title = {Carath\'eodory extremal functions on the symmetrized bidisc},
author = {Jim Agler and Zinaida Lykova and N. J. Young},
journal= {arXiv preprint arXiv:1712.00749},
year = {2018}
}
Comments
24 pages, 1 figure. This version contains some minor changes. It is to appear in a volume of Operator Theory: Advamces and Applications, Birkhauser