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arXiv · 2410.12094

Angelesco and AT systems on the Unit Circle

Rostyslav Kozhan·Marcus Vaktnäs
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Abstract

We introduce the concept of Laurent multiple orthogonality on the unit circle and define Angelesco and AT systems in this setting. Using a generalized Andreief identity, we establish normality of all multi-indices for any such system, thereby ensuring existence and uniqueness of Laurent multiple orthogonal polynomials of type I and type II at every location. As an application, we demonstrate existence and uniqueness of the approximants for two natural two-point Hermite-Pad\'e problems -- type I and type II -- arising in the simultaneous rational approximation of $r$ Carath\'{e}odory functions.

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Rostyslav Kozhan, Marcus Vaktnäs. 2024-10-15. Angelesco and AT systems on the Unit Circle. https://arxiv.org/abs/2410.12094

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