Asymptotics of Chebyshev polynomials, II: DCT subsets of R

Jacob S. Christiansen; Barry Simon; Peter Yuditskii; Maxim Zinchenko

doi:10.1215/00127094-2018-0045

Abstract

We prove Szegő–Widom asymptotics for the Chebyshev polynomials of a compact subset of $\mathbb{R}$ which is regular for potential theory and obeys the Parreau–Widom and DCT conditions.

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Jacob S. Christiansen. Barry Simon. Peter Yuditskii. Maxim Zinchenko. "Asymptotics of Chebyshev polynomials, II: DCT subsets of ${\mathbb{R}}$ ." Duke Math. J. 168 (2) 325 - 349, 1 February 2019. https://doi.org/10.1215/00127094-2018-0045

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Received: 19 March 2018; Revised: 27 August 2018; Published: 1 February 2019

First available in Project Euclid: 9 January 2019

zbMATH: 07036864

MathSciNet: MR3909898

Digital Object Identifier: 10.1215/00127094-2018-0045

Subjects:

Primary: 41A50

Secondary: 30C10 , 30E15

Keywords: Chebyshev polynomials , Direct Cauchy Theorem , Parreau–Widom set , Totik–Widom bound , Widom conjecture

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