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arXiv · 2510.17658

Schur-Agler class and Carath\'eodory extremal functions

Anindya Biswas
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Abstract

We study the role of Carath\'eodory extremal functions in the Schur-Agler class generated by a collection of test functions. We show that under certain conditions, $\mathbb{D}$ and $\mathbb{D}^2$ are the only domains where finitely many test functions can generate the Schur class. As applications, we give a description of the Carath\'eodory extremals in the unit ball of the multiplier algebra of the Drury-Arveson space and give operator-theoretic Herglotz representations for any Carath\'eodory hyperbolic domain.

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Anindya Biswas. 2025-10-20. Schur-Agler class and Carath\'eodory extremal functions. https://arxiv.org/abs/2510.17658

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