Widom Factors and Szeg\H{o}-Widom Asymptotics, a Review

TL;DR

This paper reviews the work of H. Widom on Chebyshev polynomials, focusing on their asymptotic behavior, norm bounds, and related open problems in the field.

Contribution

It provides a comprehensive survey of Widom's results on Chebyshev polynomial asymptotics and highlights open problems for future research.

Findings

Asymptotic formulas for Chebyshev polynomials

Bounds for polynomial norms

Identification of open problems in the field

Abstract

We survey results on Chebyshev polynomials centered around the work of H. Widom. In particular, we discuss asymptotics of the polynomials and their norms and general upper and lower bounds for the norms. Several open problems are also presented.