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Monotonicity of zeros of Jacobi-Angelesco polynomials


Author: Eliel J. C. dos Santos
Journal: Proc. Amer. Math. Soc. 145 (2017), 4741-4750
MSC (2010): Primary 33C45, 26C10
DOI: https://doi.org/10.1090/proc/13319
Published electronically: August 1, 2017
MathSciNet review: 3691991
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Abstract: We study the monotonic behaviour of the zeros of the multiple Jacobi-Angelesco orthogonal polynomials, in the diagonal case, with respect to the parameters $\alpha ,\beta$ and $\gamma$. We prove that the zeros are monotonic functions of $\alpha$ and $\gamma$ and consider some special cases of how the zeros depend on $\beta$, especially in the presence of symmetry. As a consequence we obtain results about monotonicity of zeros of Jacobi-Laguerre and Laguerre-Hermite multiple orthogonal polynomials too.


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Additional Information

Eliel J. C. dos Santos
Affiliation: IMECC, Universidade Estadual de Campinas, Campinas-SP, 13083-859 Brazil
MR Author ID: 1138359
Email: elielubarana@gmail.com

Keywords: Jacobi-Angelesco polynomials, zeros, monotonicity
Received by editor(s): March 11, 2016
Received by editor(s) in revised form: May 13, 2016
Published electronically: August 1, 2017
Additional Notes: The author’s research was supported by the Brazilian Science Foundation CAPES
Communicated by: Mourad E. H. Ismail
Article copyright: © Copyright 2017 American Mathematical Society