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arXiv · 2512.02670

Models of holomorphic functions on the symmetrized skew bidisc

Connor Evans·Zinaida A. Lykova·N. J. Young
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Abstract

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

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Connor Evans, Zinaida A. Lykova, N. J. Young. 2025-12-02. Models of holomorphic functions on the symmetrized skew bidisc. https://arxiv.org/abs/2512.02670

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