Norm estimates for Chebyshev polynomials, II

Klaus Schiefermayr; Maxim Zinchenko

doi:10.1016/j.jmaa.2022.126131

Norm estimates for Chebyshev polynomials, II

Klaus Schiefermayr, Maxim Zinchenko

Research Center Wels

Research output: Contribution to journal › Article › peer-review

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Abstract

In this paper, we derive upper and lower bounds for the norm of Chebyshev polynomials on subsets of the unit circle symmetric with respect to the real line. In the case of two circular arcs symmetric with respect to the origin we find asymptotics of the corresponding Widom factors and obtain exact values of their supremum and infimum.

Original language	English
Article number	126131
Journal	Journal of Mathematical Analysis and Applications
Volume	512
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2022.126131
Publication status	Published - 1 Aug 2022

Keywords

Chebyshev polynomials on symmetric subsets of the unit circle
Lower and upper bounds on Widom factors

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10.1016/j.jmaa.2022.126131

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title = "Norm estimates for Chebyshev polynomials, II",

abstract = "In this paper, we derive upper and lower bounds for the norm of Chebyshev polynomials on subsets of the unit circle symmetric with respect to the real line. In the case of two circular arcs symmetric with respect to the origin we find asymptotics of the corresponding Widom factors and obtain exact values of their supremum and infimum.",

keywords = "Chebyshev polynomials on symmetric subsets of the unit circle, Lower and upper bounds on Widom factors",

author = "Klaus Schiefermayr and Maxim Zinchenko",

note = "Funding Information: M.Z. was supported in part by Simons Foundation grant CGM–581256. Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",

year = "2022",

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AU - Schiefermayr, Klaus

AU - Zinchenko, Maxim

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N2 - In this paper, we derive upper and lower bounds for the norm of Chebyshev polynomials on subsets of the unit circle symmetric with respect to the real line. In the case of two circular arcs symmetric with respect to the origin we find asymptotics of the corresponding Widom factors and obtain exact values of their supremum and infimum.

AB - In this paper, we derive upper and lower bounds for the norm of Chebyshev polynomials on subsets of the unit circle symmetric with respect to the real line. In the case of two circular arcs symmetric with respect to the origin we find asymptotics of the corresponding Widom factors and obtain exact values of their supremum and infimum.

KW - Chebyshev polynomials on symmetric subsets of the unit circle

KW - Lower and upper bounds on Widom factors

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DO - 10.1016/j.jmaa.2022.126131

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VL - 512

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JF - Journal of Mathematical Analysis and Applications

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Norm estimates for Chebyshev polynomials, II

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Keywords

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