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arXiv · 1708.05781

Universality at an Endpoint for Orthogonal Polynomials with Geronimus-Type Weights

Brian Simanek
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Abstract

We provide a new closed form expression for the Geronimus polynomials on the unit circle and use it to obtain new results and formulas. Among our results is a universality result at an endpoint of an arc for polynomials orthogonal with respect to a Geronimus type weight on an arc of the unit circle. The key tool is a formula of McLaughlin for powers of a two-by-two matrix, which we use to derive convenient formulas for Geronimus polynomials.

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Brian Simanek. 2017-08-18. Universality at an Endpoint for Orthogonal Polynomials with Geronimus-Type Weights. https://doi.org/10.1090/proc%2F14085

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