Riemann-Hilbert analysis for a Nikishin system

Abstract

In this paper we give the asymptotic behavior of type I multiple orthogonal polynomials for a Nikishin system of order two with two disjoint intervals. We use the Riemann-Hilbert problem for multiple orthogonal polynomials and the steepest descent analysis for oscillatory Riemann-Hilbert problems to obtain the asymptotic behavior in all relevant regions of the complex plane.

30 pages, 7 figures

References in corpus (2)

• Strong Asymptotics of Hermite-Padé Approximants for Angelesco Systems
• Hermite-Padé approximants for a pair of Cauchy transforms with overlapping symmetric supports

Cited by in corpus (2)

• Riemann-Hilbert Characterisation of Rational Functions with a General Distribution of Poles on the Extended Real Line Orthogonal with Respect to Varying Exponential Weights: Multi-Point Padé Approximants and Asymptotics
• On a new approach to the problem of the zero distribution of Hermite-Padé polynomials for a Nikishin system