On Nikishin systems with discrete components and weak asymptotics of multiple orthogonal polynomials

Abstract

We consider multiple orthogonal polynomials with respect to Nikishin systems generated by two measures $({\sigma }_1,{\sigma }_2)$ with unbounded supports ($\mbox{supp} \, σ_1 \subseteq \mathbb{R}_+$, $\mbox{supp} \, σ_2 \subseteq \,\mathbb{R}_-$) and ${\sigma }_2$ is discrete. A Nikishin type equilibrium problem in the presence of an external field acting on ${\mathbb{R}}_{+}$ and a constraint on ${\mathbb{R}}_{-}$ is stated and solved. The solution is used for deriving the contracted zero distribution of the associated multiple orthogonal polynomials.

47 pages, 1 figure

References in corpus (1)

• Weakly Admissible Vector Equilibrium Problems