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Ahlfors problem for polynomials

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Ahlfors problem for polynomials. / Eichinger, B.; Yuditskii, P.
In: Sbornik Mathematics, Vol. 209, No. 3, 2018, p. 320-351.

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

Harvard

Eichinger, B & Yuditskii, P 2018, 'Ahlfors problem for polynomials', Sbornik Mathematics, vol. 209, no. 3, pp. 320-351. https://doi.org/10.1070/SM8878

APA

Eichinger, B., & Yuditskii, P. (2018). Ahlfors problem for polynomials. Sbornik Mathematics, 209(3), 320-351. https://doi.org/10.1070/SM8878

Vancouver

Eichinger B, Yuditskii P. Ahlfors problem for polynomials. Sbornik Mathematics. 2018;209(3):320-351. doi: 10.1070/SM8878

Author

Eichinger, B. ; Yuditskii, P. / Ahlfors problem for polynomials. In: Sbornik Mathematics. 2018 ; Vol. 209, No. 3. pp. 320-351.

Bibtex

@article{5f2852bbf9a04027a9708e8ed0576865,
title = "Ahlfors problem for polynomials",
abstract = "We present a conjecture that the asymptotics for Chebyshev polynomials in a complex domain can be given in terms of the reproducing kernels of a suitable Hilbert space of analytic functions in this domain. It is based on two classical results due to Garabedian and Widom. To support this conjecture we study the asymptotics for Ahlfors extremal polynomials in the complement to a system of intervals on R, arcs on T, and the asymptotics of the extremal entire functions for the continuous counterpart of this problem. Bibliography: 35 titles.",
keywords = "Abel-Jacobi inversion, analytic capacity, Chebyshev polynomial, complex Greens and Martin functions, hyperelliptic Riemann surface, reproducing kernel.",
author = "B. Eichinger and P. Yuditskii",
note = "Publisher Copyright: {\textcopyright} 2018 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.",
year = "2018",
doi = "10.1070/SM8878",
language = "English",
volume = "209",
pages = "320--351",
journal = "Sbornik Mathematics",
issn = "1064-5616",
publisher = "Steklov Mathematical Institute of Russian Academy of Sciences",
number = "3",

}

RIS

TY - JOUR

T1 - Ahlfors problem for polynomials

AU - Eichinger, B.

AU - Yuditskii, P.

N1 - Publisher Copyright: © 2018 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.

PY - 2018

Y1 - 2018

N2 - We present a conjecture that the asymptotics for Chebyshev polynomials in a complex domain can be given in terms of the reproducing kernels of a suitable Hilbert space of analytic functions in this domain. It is based on two classical results due to Garabedian and Widom. To support this conjecture we study the asymptotics for Ahlfors extremal polynomials in the complement to a system of intervals on R, arcs on T, and the asymptotics of the extremal entire functions for the continuous counterpart of this problem. Bibliography: 35 titles.

AB - We present a conjecture that the asymptotics for Chebyshev polynomials in a complex domain can be given in terms of the reproducing kernels of a suitable Hilbert space of analytic functions in this domain. It is based on two classical results due to Garabedian and Widom. To support this conjecture we study the asymptotics for Ahlfors extremal polynomials in the complement to a system of intervals on R, arcs on T, and the asymptotics of the extremal entire functions for the continuous counterpart of this problem. Bibliography: 35 titles.

KW - Abel-Jacobi inversion

KW - analytic capacity

KW - Chebyshev polynomial

KW - complex Greens and Martin functions

KW - hyperelliptic Riemann surface

KW - reproducing kernel.

U2 - 10.1070/SM8878

DO - 10.1070/SM8878

M3 - Journal article

AN - SCOPUS:85048104574

VL - 209

SP - 320

EP - 351

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 3

ER -