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Pointwise Remez inequality

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Pointwise Remez inequality. / Eichinger, B.; Yuditskii, P.
In: Constructive Approximation, Vol. 54, No. 3, 31.12.2021, p. 529-554.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Eichinger, B & Yuditskii, P 2021, 'Pointwise Remez inequality', Constructive Approximation, vol. 54, no. 3, pp. 529-554. https://doi.org/10.1007/s00365-021-09562-1

APA

Eichinger, B., & Yuditskii, P. (2021). Pointwise Remez inequality. Constructive Approximation, 54(3), 529-554. https://doi.org/10.1007/s00365-021-09562-1

Vancouver

Eichinger B, Yuditskii P. Pointwise Remez inequality. Constructive Approximation. 2021 Dec 31;54(3):529-554. Epub 2021 Nov 8. doi: 10.1007/s00365-021-09562-1

Author

Eichinger, B. ; Yuditskii, P. / Pointwise Remez inequality. In: Constructive Approximation. 2021 ; Vol. 54, No. 3. pp. 529-554.

Bibtex

@article{8316c5eed4814f1e914c2f6427ddcf18,
title = "Pointwise Remez inequality",
abstract = "The standard well-known Remez inequality gives an upper estimate of the values of polynomials on [- 1 , 1] if they are bounded by 1 on a subset of [- 1 , 1] of fixed Lebesgue measure. The extremal solution is given by the rescaled Chebyshev polynomials for one interval. Andrievskii asked about the maximal value of polynomials at a fixed point, if they are again bounded by 1 on a set of fixed size. We show that the extremal polynomials are either Chebyshev (one interval) or Akhiezer polynomials (two intervals) and prove Totik–Widom bounds for the extremal value, thereby providing a complete asymptotic solution to the Andrievskii problem.",
keywords = "Chebyshev and Akhiezer polynomials, Comb domains, Remez inequality, Totik–Widom bounds",
author = "B. Eichinger and P. Yuditskii",
note = "Publisher Copyright: {\textcopyright} 2021, The Author(s).",
year = "2021",
month = dec,
day = "31",
doi = "10.1007/s00365-021-09562-1",
language = "English",
volume = "54",
pages = "529--554",
journal = " Constructive Approximation",
issn = "0176-4276",
publisher = "Springer",
number = "3",

}

RIS

TY - JOUR

T1 - Pointwise Remez inequality

AU - Eichinger, B.

AU - Yuditskii, P.

N1 - Publisher Copyright: © 2021, The Author(s).

PY - 2021/12/31

Y1 - 2021/12/31

N2 - The standard well-known Remez inequality gives an upper estimate of the values of polynomials on [- 1 , 1] if they are bounded by 1 on a subset of [- 1 , 1] of fixed Lebesgue measure. The extremal solution is given by the rescaled Chebyshev polynomials for one interval. Andrievskii asked about the maximal value of polynomials at a fixed point, if they are again bounded by 1 on a set of fixed size. We show that the extremal polynomials are either Chebyshev (one interval) or Akhiezer polynomials (two intervals) and prove Totik–Widom bounds for the extremal value, thereby providing a complete asymptotic solution to the Andrievskii problem.

AB - The standard well-known Remez inequality gives an upper estimate of the values of polynomials on [- 1 , 1] if they are bounded by 1 on a subset of [- 1 , 1] of fixed Lebesgue measure. The extremal solution is given by the rescaled Chebyshev polynomials for one interval. Andrievskii asked about the maximal value of polynomials at a fixed point, if they are again bounded by 1 on a set of fixed size. We show that the extremal polynomials are either Chebyshev (one interval) or Akhiezer polynomials (two intervals) and prove Totik–Widom bounds for the extremal value, thereby providing a complete asymptotic solution to the Andrievskii problem.

KW - Chebyshev and Akhiezer polynomials

KW - Comb domains

KW - Remez inequality

KW - Totik–Widom bounds

U2 - 10.1007/s00365-021-09562-1

DO - 10.1007/s00365-021-09562-1

M3 - Journal article

AN - SCOPUS:85118598857

VL - 54

SP - 529

EP - 554

JO - Constructive Approximation

JF - Constructive Approximation

SN - 0176-4276

IS - 3

ER -