2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65064Let $p_n(x)$ be orthogonal polynomials associated to a measure $dμ$ of compact support in $R$. If $E\not\in supp(dμ)$, we show there is a $δ>0$ so that for all $n$, either $p_n$ or $p_{n+1}$ has no zeros in $(E-δ, E+δ)$. If $E$ is an isolated point of $supp(dμ)$, we show there is a $δ$ so that for all $n$, either $p_n$ or $p_{n+1}$ has at most one zero in $(E-δ, E+δ)$. We provide an example where the zeros of $p_n$ are dense in a gap of $supp(dμ)$.(preliminary version)Classical Analysis and ODEsMathematical Physics42C05, 47B36text