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arXiv · 1108.6130

On the zeros of orthogonal polynomials on the unit circle

María Pilar Alfaro·Manuel Bello-Hernández·Jesús María Montaner
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Abstract

Let ${z_n}$ be a sequence in the unit disk ${z\in\mathbb{C}:|z|<1}$. It is known that there exists a unique positive Borel measure in the unit circle ${z\in\mathbb{C}:|z|=1}$ such that the orthogonal polynomials ${Φ_n}$ satisfy [Φ_n(z_n)=0] for each $n=1,2,...$. Characteristics of the orthogonality measure and asymptotic properties of the orthogonal polynomial are given in terms of asymptotic behavior of the sequence ${z_n}$. Particular attention is paid to periodic sequence of zeros ${z_n}$ of period two and three.

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María Pilar Alfaro, Manuel Bello-Hernández, Jesús María Montaner. 2011-09-20. On the zeros of orthogonal polynomials on the unit circle. https://arxiv.org/abs/1108.6130

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