Relative Asymptotics for General Orthogonal Polynomials

TL;DR

This paper investigates the asymptotic behavior of orthogonal polynomials through the analysis of the Bergman Shift matrix, providing insights into their ratio limits, zero distributions, and related measures.

Contribution

It introduces new results on the right limits of the Bergman Shift matrix and their implications for various asymptotic properties of orthogonal polynomials.

Findings

Characterization of right limits of the Bergman Shift matrix

Applications to ratio asymptotics and zero counting measures

Insights into weak asymptotic measures and relative asymptotics

Abstract

We study right limits of the Bergman Shift matrix. Our results have applications to ratio asymptotics, weak asymptotic measures, relative asymptotics, and zero counting measures of the orthogonal and orthonormal polynomials.