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

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

2007-07-13

arxiv.org/abs/0707.1996v1

Mathematics

Complex Variables

24 pages, 2 tables

Scientific paper

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 $\widetilde{\Delta}_k$, on which $\sigma_k^{\prime} > 0$ almost everywhere, and a set without accumulation points in $\mathbb{R} \setminus \widetilde{\Delta}_k$.

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