Chebyshev polynomials on a Jordan arc

Benedikt Buchecker; Benjamin Eichinger; Olof Rubin; Aron Wennman

Chebyshev polynomials on a Jordan arc

经典分析与常微分方程 2026-08-13 v1 复变函数

作者: Benedikt Buchecker , Benjamin Eichinger , Olof Rubin , Aron Wennman

摘要

We describe the asymptotics of Chebyshev polynomials on an analytic Jordan arc in the plane. This gives an affirmative answer to a conjecture of Christiansen-Simon-Zinchenko, based on predictions of Widom from 1969. The proof combines weighted Faber polynomials with extremal signatures, discrete orthogonal polynomials and a Marcinkiewicz-Zygmund sampling inequality, and yields Szeg\H{o}-Widom asymptotics for the Chebyshev polynomials themselves.

引用

@article{arxiv.2608.13445,
  title  = {Chebyshev polynomials on a Jordan arc},
  author = {Benedikt Buchecker and Benjamin Eichinger and Olof Rubin and Aron Wennman},
  journal= {arXiv preprint arXiv:2608.13445},
  year   = {2026}
}