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arXiv · 2608.00827

Function theoretic aspects of the symmetrized polydisc and generalization

Sourav Pal·Nitin Tomar
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Abstract

We introduce Schur-Agler type class for the symmetrized polydisc $\mathbb{G}_d$ and establish a realization theorem for functions in this class. We state and prove an interpolation theorem on $\mathbb{G}_d$ with interpolating functions belonging to the associated Schur-Agler type class. Moreover, Toeplitz corona and extension theorems are established for $\mathbb{G}_d$. We also extend the realization, interpolation, Toeplitz corona and extension theorems to a more general symmetrized family of domains $\Theta_d$.

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Sourav Pal, Nitin Tomar. 2026-08-01. Function theoretic aspects of the symmetrized polydisc and generalization. https://arxiv.org/abs/2608.00827

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