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We investigate polynomials that satisfy simultaneous orthogonality conditions with respect to several measures on the unit circle. We generalize the direct and inverse Szego recurrence relations, identify the analogues of the Verblunsky coefficients, and prove the Christoffelx2013Darboux formula. These results stand directly in analogue with the nearest neighbour recurrence relations from the real line counterpart.
Kozhan et al. (Fri,) studied this question.
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