Journal of Approximation Theory
| Hi-index | 0.00 |
We prove the relative asymptotic behavior for the ratio of two sequences of multiple orthogonal polynomials with respect to the Nikishin systems of measures. The first Nikishin system N(@s"1,...,@s"m) is such that for each k, @s"k has a constant sign on its compact support supp(@s"k)@?R consisting of an interval @D@?"k, on which |@s"k^'|0 almost everywhere, and a discrete set without accumulation points in R@?@D@?"k. If Co(supp(@s"k))=@D"k denotes the smallest interval containing supp(@s"k), we assume that @D"k@?@D"k"+"1=0@?, k=1,...,m-1. The second Nikishin system N(r"1@s"1,...,r"m@s"m) is a perturbation of the first by means of rational functions r"k, k=1,...,m, whose zeros and poles lie in C@?@?"k"="1^m@D"k.