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arXiv · 2404.18666

Szeg\H{o} Recurrence for Multiple Orthogonal Polynomials on the Unit Circle

Marcus Vaktnäs·Rostyslav Kozhan
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Abstract

We investigate polynomials that satisfy simultaneous orthogonality conditions with respect to several measures on the unit circle. We generalize the direct and inverse Szeg\H{o} recurrence relations, identify the analogues of the Verblunsky coefficients, and prove the Christoffel$\unicode{x2013}$Darboux formula. These results stand directly in analogue with the nearest neighbour recurrence relations from the real line counterpart.

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Marcus Vaktnäs, Rostyslav Kozhan. 2024-04-29. Szeg\H{o} Recurrence for Multiple Orthogonal Polynomials on the Unit Circle. https://doi.org/10.1090/proc%2F16811

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