Majorization results for zeros of orthogonal polynomials

Van Assche, Walter

doi:10.1090/proc/13560

Majorization results for zeros of orthogonal polynomials
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by Walter Van Assche PDF

Proc. Amer. Math. Soc. 145 (2017), 3849-3863 Request permission

Abstract:

We show that the zeros of consecutive orthogonal polynomials $p_n$ and $p_{n-1}$ are linearly connected by a doubly stochastic matrix for which the entries are explicitly computed in terms of Christoffel numbers. We give similar results for the zeros of $p_n$ and the associated polynomial $p_{n-1}^{(1)}$ and for the zeros of the polynomial obtained by deleting the $k$th row and column $(1 \leq k \leq n)$ in the corresponding Jacobi matrix.

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