Universality at an endpoint for orthogonal polynomials with Geronimus-type weights

Simanek, Brian

doi:10.1090/proc/14085

Universality at an endpoint for orthogonal polynomials with Geronimus-type weights
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Proc. Amer. Math. Soc. 146 (2018), 3995-4007 Request permission

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 the $n^{th}$ power of a $2\times 2$ matrix, which we use to derive convenient formulas for Geronimus polynomials.

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