On the zeros of orthogonal polynomials on the unit circle

Details On the zeros of orthogonal polynomials on the unit circle On the zeros of orthogonal polynomials on the unit circle

2011-08-31

arxiv.org/abs/1108.6130v2

Mathematics

Classical Analysis and ODEs

25 pages. Summited for publication. Some typos have been corrected

Scientific paper

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 ${\Phi_n}$ satisfy [\Phi_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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