Riemann-Hilbert analysis for a Nikishin system

TL;DR

This paper analyzes the asymptotic behavior of type I multiple orthogonal polynomials in a Nikishin system using Riemann-Hilbert techniques and steepest descent analysis, providing detailed asymptotics across the complex plane.

Contribution

It introduces a Riemann-Hilbert approach combined with steepest descent analysis to derive asymptotics for multiple orthogonal polynomials in Nikishin systems.

Findings

Asymptotic formulas for type I multiple orthogonal polynomials

Uniform asymptotic behavior across complex regions

Application of Riemann-Hilbert steepest descent method

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.