Relative Asymptotic of Multiple Orthogonal Polynomials for Nikishin Systems

Details Relative Asymptotic of Multiple Orthogonal Polynomials for Nikishin Systems Relative Asymptotic of Multiple Orthogonal Polynomials for Nikishin Systems

2008-02-05

arxiv.org/abs/0802.0722v1

Mathematics

Complex Variables

30 pages

Scientific paper

We prove relative asymptotic for the ratio of two sequences of multiple orthogonal polynomials with respect to Nikishin system of measures. The first Nikishin system ${\mathcal{N}}(\sigma_1,...,\sigma_m)$ is such that for each $k$, $\sigma_k$ has constant sign on its compact support $\supp {\sigma_k} \subset \mathbb{R}$ consisting of an interval $\widetilde{\Delta}_k$, on which $|\sigma_k^{\prime}| > 0$ almost everywhere, and a discrete set without accumulation points in $\mathbb{R} \setminus \widetilde{\Delta}_k$. If ${Co}(\supp {\sigma_k}) = \Delta_k$ denotes the smallest interval containing $\supp {\sigma_k}$, we assume that $\Delta_k \cap \Delta_{k+1} = \emptyset$, $k=1,...,m-1$. The second Nikishin system ${\mathcal{N}}(r_1\sigma_1,...,r_m\sigma_m)$ is a perturbation of the first by means of rational functions $r_k$, $k=1,...,m,$ whose zeros and poles lie in $\mathbb{C} \setminus \cup_{k=1}^m \Delta_k$.

Affiliated with

Also associated with

No associations

Rating

Relative Asymptotic of Multiple Orthogonal Polynomials for Nikishin Systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Relative Asymptotic of Multiple Orthogonal Polynomials for Nikishin Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Relative Asymptotic of Multiple Orthogonal Polynomials for Nikishin Systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-559532