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Gradient system for the roots of the Askey-Wilson polynomial


Author: J. F. van Diejen
Journal: Proc. Amer. Math. Soc. 147 (2019), 5239-5249
MSC (2010): Primary 33D45; Secondary 26C10, 34D05, 34D23
DOI: https://doi.org/10.1090/proc/14625
Published electronically: July 1, 2019
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Abstract: Recently, it was observed that the roots of the Askey-Wilson polynomial are retrieved at the unique global minimum of an associated strictly convex Morse function [J. F. van Diejen and E. Emsiz, Lett. Math. Phys. 109 (2019), pp. 89-112]. The purpose of the present note is to infer that the corresponding gradient flow converges to the roots in question at an exponential rate.


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Additional Information

J. F. van Diejen
Affiliation: Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile
Email: diejen@inst-mat.utalca.cl

DOI: https://doi.org/10.1090/proc/14625
Keywords: Askey-Wilson polynomials, zeros of orthogonal polynomials, gradient flow
Received by editor(s): December 14, 2018
Received by editor(s) in revised form: March 10, 2019
Published electronically: July 1, 2019
Additional Notes: This work was supported in part by the Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) Grant # 1170179.
Communicated by: Mourad Ismail
Article copyright: © Copyright 2019 American Mathematical Society