Relative Asymptotics for General Orthogonal Polynomials
Brian Simanek

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.
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