Weighted residual polynomials on a circular arc

TL;DR

This paper investigates the asymptotic behavior of weighted residual polynomials on circular arcs, including Chebyshev and Widom factors, extending existing results to less regular weights and specific lemniscatic arcs.

Contribution

It generalizes Szeg\

Findings

Established Szeg\

Determined asymptotics of weighted Widom factors for less regular weights

Derived asymptotics of Widom factors on lemniscatic arcs

Abstract

We study the behavior of weighted residual polynomials on circular arcs, including weighted Chebyshev polynomials. For weights given by reciprocals of polynomials, we establish Szeg\H{o}-Widom asymptotics. Extending our analysis to less regular weights, we determine the asymptotic behavior of the corresponding weighted Widom factors, generalizing results by Eichinger and Thiran et al. As an application, we derive the asymptotics of Widom factors on certain lemniscatic arcs.