Asymptotics of Chebyshev Polynomials, III. Sets Saturating Szeg\H{O}, Schiefermayr, and Totik--Widom Bounds

TL;DR

This paper characterizes the sets that achieve equality in key bounds for Chebyshev polynomials, advancing understanding of polynomial extremal problems in approximation theory.

Contribution

It identifies the specific sets that saturate the Szeg o, Schiefermayr, and Totik--Widom bounds, providing a complete characterization of extremal sets.

Findings

Sets saturating Szeg o and Schiefermayr bounds are characterized.

Sets saturating the Totik--Widom upper bound are discussed.

The paper advances the theory of Chebyshev polynomial extremal sets.

Abstract

We determine which sets saturate the Szeg}o and Schiefermayr lower bounds on the norms of Chebyshev Polynomials. We also discuss sets that saturate the Totik--Widom upper bound.