# Asymptotics for polynomials orthogonal in an indefinite metric

## TL;DR

This paper investigates the asymptotic behavior of orthogonal polynomials generated by Szeg\

## Contribution

It extends asymptotic analysis to polynomials with Verblunsky coefficients outside the unit disk, linking complex and real line cases.

## Key findings

- Established asymptotics for polynomials with non-standard Verblunsky coefficients.
- Translated complex-plane results to real-line Szeg\
- Showed the associated matrix is a finite-rank perturbation of a symmetric Jacobi matrix.

## Abstract

We continue studying polynomials generated by the Szeg\H{o} recursion when a finite number of Verblunsky coefficients lie outside the closed unit disk. We prove some asymptotic results for the corresponding orthogonal polynomials and then translate them to the real line to obtain the Szeg\H{o} asymptotics for the resulting polynomials. The latter polynomials give rise to a non-symmetric tridiagonal matrix but it is a finite-rank perturbation of a symmetric Jacobi matrix.