Ahlfors problem for polynomials

Benjamin Eichinger, Peter Yuditskii

Type: Article

Publication Date: 2017-08-18

Citations: 8

DOI: https://doi.org/10.1070/sm8878

Abstract

We raise a conjecture that 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 asymptotics for Ahlfors extremal polynomials in the complement to a system of intervals on $\mathbb R$, arcs on $\mathbb T$, and its continuous counterpart.

Locations

arXiv (Cornell University) - View - PDF
Sbornik Mathematics - View

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