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Mat. Sb., 2018, Volume 209, Number 3, Pages 34–66 (Mi msb8878)  

This article is cited in 1 scientific paper (total in 1 paper)

Ahlfors problem for polynomials

B. Eichingera, P. Yuditskiib

a Institute of Analysis, Johannes Kepler University Linz, Austria
b Section Dynamical Systems and Approximation Theory, Institute of Analysis, Johannes Kepler University Linz, Austria

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 $\mathbb{R}$, arcs on $\mathbb{T}$, and the asymptotics of the extremal entire functions for the continuous counterpart of this problem.
Bibliography: 35 titles.

Keywords: Chebyshev polynomial, analytic capacity, hyperelliptic Riemann surface, Abel-Jacobi inversion, complex Green's and Martin functions, reproducing kernel.

Funding Agency Grant Number
Austrian Science Fund P25591-N25
This research was supported by the Austrian Science Fund FWF (project no. P25591-N25).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8878

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English version:
Sbornik: Mathematics, 2018, 209:3, 320–351

Bibliographic databases:

UDC: 517.535.2+517.54
MSC: Primary 30C10, 30E15, 41A50; Secondary 14K20, 30C85, 30F10, 46E22
Received: 09.12.2016 and 14.04.2017

Citation: B. Eichinger, P. Yuditskii, “Ahlfors problem for polynomials”, Mat. Sb., 209:3 (2018), 34–66; Sb. Math., 209:3 (2018), 320–351

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Christiansen J.S., Simon B., Yuditskii P., Zinchenko M., “Asymptotics of Chebyshev Polynomials, II: Dct Subsets of R”, Duke Math. J., 168:2 (2019), 325–349  crossref  mathscinet  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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