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Sbornik: Mathematics, 2018, Volume 209, Issue 3, Pages 320–351
DOI: https://doi.org/10.1070/SM8878 (Mi sm8878) 		 
This article is cited in 6 scientific papers (total in 6 papers)

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
English version PDF (738 kB) Citations (6)
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DOI: https://doi.org/10.1070/SM8878
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).
Received: 09.12.2016 and 14.04.2017
Russian version:
Matematicheskii Sbornik, 2018, Volume 209, Number 3, Pages 34–66
DOI: https://doi.org/10.4213/sm8878
Bibliographic databases:
Document Type: Article
UDC: 517.535.2+517.54
MSC: Primary 30C10, 30E15, 41A50; Secondary 14K20, 30C85, 30F10, 46E22
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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