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arXiv · 1501.07235

Monotonicity of zeros of polynomials orthogonal with respect to a discrete measure

Dimitar K. Dimitrov
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Abstract

We prove that all zeros of the polynomials orthogonal with respect to a measure $d μ(x;a) = d μ(x) + M δ(x-a)$, where $dμ$ is a nonatomic positive Borel measure and $M>0$, are increasing functions of the mass point $a$. Thus we solve partially an open problem posed by Mourad Ismail.

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Dimitar K. Dimitrov. 2015-01-28. Monotonicity of zeros of polynomials orthogonal with respect to a discrete measure. https://arxiv.org/abs/1501.07235

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