单位圆上多重正交多项式的 Szegő 递推法

arXiv - MATH - Spectral Theory Pub Date : 2024-04-29 DOI:arxiv-2404.18666

Marcus Vaktnäs, Rostyslav Kozhan

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引用次数: 0

摘要

我们研究了与单位圆上的几个度量同时满足正交条件的多项式。我们概括了 Szeg\H{o} 的直接和逆递推关系，确定了 Verblunsky 系数的类比，并证明了 Christoffel$/unicode{x2013}$Darboux 公式。这些结果与实线对应的近邻递推关系直接对应。

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Szegő Recurrence for Multiple Orthogonal Polynomials on the Unit Circle

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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arXiv - MATH - Spectral Theory

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