Ratio Asymptotic of Hermite-Padé Orthogonal Polynomials for Nikishin Systems. II

Abstract

We prove ratio asymptotic for sequences of multiple orthogonal polynomials with respect to a Nikishin system of measures $\mathcal{N}({\sigma }_1,...,{\sigma }_m)$ such that for each $k$, the support of ${\sigma }_k$ consists of an interval ${\tilde{\Delta }}_k$, on which ${\sigma }_k^{\prime }>0$ almost everywhere, and a set without accumulation points in $\mathbb{R}\setminus {\tilde{\Delta }}_k$.

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