Uniform algebras and distinguished varieties

Sushil Gorai; Golam Mostafa Mondal

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arXiv · 2309.05006

Uniform algebras and distinguished varieties

Sushil Gorai·Golam Mostafa Mondal

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Abstract

In this article, we point out the connections between the distinguished varieties introduced by Agler and McCarthy with certain uniform algebras on bidisc studied by Samuelsson and Wold. We also prove analogues of Samuelsson-Wold result for the domains in $\mathbb{C}^2$ that are the images of the bidisc under certain proper polynomial map on $\mathbb{C}^2$. We also give a description of polynomial convex hull of graph of anti-holomorphic polynomial over the distinguished boundary of such domains. We mention the case for the symmetrized bidisc as an example.

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Sushil Gorai, Golam Mostafa Mondal. 2023-09-10. Uniform algebras and distinguished varieties. https://arxiv.org/abs/2309.05006

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