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arXiv · 2608.13445

Chebyshev polynomials on a Jordan arc

Benedikt Buchecker·Benjamin Eichinger·Olof Rubin·Aron Wennman
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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 Szeg\H{o}-Widom asymptotics for the Chebyshev polynomials themselves.

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Benedikt Buchecker, Benjamin Eichinger, Olof Rubin, Aron Wennman. 2026-08-13. Chebyshev polynomials on a Jordan arc. https://arxiv.org/abs/2608.13445

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