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

Abstract

We prove that all zeros of the polynomials orthogonal with respect to a measure $d \mu(x;a) = d \mu(x) + M \delta(x-a)$, where $d\mu$ 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.