Models of holomorphic functions on the symmetrized skew bidisc

Abstract

The purpose of this paper is to develop the theory of holomorphic functions with modulus bounded by $1$ on the symmetrized skew bidisc \[ \mathbb{G}_{r} \stackrel{\rm def}{=} \Big\{( λ_{1}+rλ_{2} ,rλ_{1}λ_{2}): λ_{1}\in \mathbb{D}, λ_{2}\in\mathbb{D}\Big\}, \] for a fixed $r\in (0,1)$. We show the existence of a realization formula and a model formula for such holomorphic functions.

22 pages. This version is a slight modification of the original paper following a referee report. It will appear in the Journal "Integral Equations and Operator Theory"