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Proceedings of the American Mathematical Society

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


Author: Brian Simanek
Journal: Proc. Amer. Math. Soc. 146 (2018), 3995-4007
MSC (2010): Primary 42C05; Secondary 33C45
DOI: https://doi.org/10.1090/proc/14085
Published electronically: April 26, 2018
MathSciNet review: 3825852
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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 the $n^{th}$ power of a $2\times 2$ matrix, which we use to derive convenient formulas for Geronimus polynomials.


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Additional Information

Brian Simanek
Affiliation: Department of Mathematics, Baylor University, One Bear Place 97328, Waco, Texas 76798
MR Author ID: 959574

Keywords: Geronimus polynomials, Chebyshev polynomials, universality
Received by editor(s): August 18, 2017
Received by editor(s) in revised form: December 18, 2017
Published electronically: April 26, 2018
Communicated by: Mourad Ismail
Article copyright: © Copyright 2018 American Mathematical Society