Monotonicity of zeros of Jacobi-Angelesco polynomials

dos Santos, Eliel

doi:10.1090/proc/13319

Monotonicity of zeros of Jacobi-Angelesco polynomials
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by Eliel J. C. dos Santos PDF

Proc. Amer. Math. Soc. 145 (2017), 4741-4750 Request permission

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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