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Zero Spacings of Paraorthogonal Polynomials on the Unit Circle

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arxiv 1907.01604 v1 pith:L5NNTLKS submitted 2019-07-02 math.CA

Brian Simanek This is my paper · ORCID
classification math.CA
keywords circleunitparaorthogonalpolynomialsresultssomeappropriateblaschke
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We prove some new results about the spacing between neighboring zeros of paraorthogonal polynomials on the unit circle. Our methods also provide new proofs of some existing results. The main tool we will use is a formula for the phase of the appropriate Blaschke product at points on the unit circle.

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  1. On the spacing of zeros of paraorthogonal polynomials for singular measures

    math.SP 2019-08 conditional novelty 6.0 of 10

    The spacing of paraorthogonal polynomial zeros is bounded below by a measure's Hausdorff continuity, and sparse Verblunsky coefficients can force clock spacing even for singular continuous measures.

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