Strong Asymptotics of Multiple Orthogonal Polynomials for Angelesco Systems. Part I: Non-Marginal Directions

TL;DR

This paper derives strong asymptotic formulas for multiple orthogonal polynomials associated with Angelesco systems under Szeg ext{"o} conditions, focusing on multi-indices diverging in non-marginal directions, advancing understanding in asymptotic analysis.

Contribution

It provides the first detailed asymptotic analysis of multiple orthogonal polynomials in non-marginal directions for Angelesco systems under Szeg ext{"o} conditions.

Findings

Established strong asymptotics for non-marginal multi-indices

Extended asymptotic analysis to Angelesco systems with Szeg ext{"o} measures

Enhanced understanding of polynomial behavior in complex systems

Abstract

In this work, we establish strong asymptotics of multiple orthogonal polynomials of the second type for Angelesco systems with measures that satisfy Szeg\H{o} conditions. We consider multi-indices that converge to infinity in the non-marginal directions.