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Szegő Recurrence for Multiple Orthogonal Polynomials on the Unit Circle (2404.18666v1)
Published 29 Apr 2024 in math.CA and math.SP
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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