PreprintCC BY 4.0arXiv
Chebyshev polynomials on a Jordan arc
Abstract
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 Szegő-Widom asymptotics for the Chebyshev polynomials themselves.
Related
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- Hsiang cubics as spherical Chebyshev polynomials: equioscillation and idempotent quadrature
BibTeX
@misc{buchecker2026chebyshev,
title = {{Chebyshev polynomials on a Jordan arc}},
author = {Benedikt Buchecker and Benjamin Eichinger and Olof Rubin and Aron Wennman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.13445},
eprint = {2608.13445},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.13445},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Chebyshev polynomials on a Jordan arc
AU - Benedikt Buchecker
AU - Benjamin Eichinger
AU - Olof Rubin
AU - Aron Wennman
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2608.13445
UR - https://arxiv.org/abs/2608.13445
AB - 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 Szegő-Widom asymptotics for the Chebyshev polynomials themselves.
ER -