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arXiv · 1607.03251

Majorization results for zeros of orthogonal polynomials

Walter Van Assche
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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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Walter Van Assche. 2016-07-12. Majorization results for zeros of orthogonal polynomials. https://doi.org/10.1090/proc/13560

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