A Schwarz lemma for the symmetrized tridisc and description of interpolating functions

Abstract

We produce a Schwarz lemma for the symmetrized tridisc \[ \mathbb G_3 =\{ (z_1+z_2+z_3,z_1z_2+z_2z_3+z_3z_1,z_1z_2z_3): \,|z_i|< 1, i=1,2,3 \}. \] We show that an interpolating function related to the Schward lemma for ${\mathbb{G}}_3$ is not unique and present an explicit description of all such interpolating functions. We also study the complex geometry of ${\mathbb{G}}_3$ and present a variety of new characterizations for the open and closed symmetrized tridisc.

Error in one of the main results

References in corpus (3)

• Extremal holomorphic maps and the symmetrised bidisc
• Characterizations of Symmetrized Polydisc
• Rational dilation on the symmetrized tridisc: failure, success and unknown

Cited by in corpus (1)

• Automorphisms and the fundamental operators associated with the symmetrized tridisc