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arXiv · 2101.01744

Asymptotics of Chebyshev rational functions with respect to subsets of the real line

Benjamin Eichinger·Milivoje Lukić·Giorgio Young
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Abstract

There is a vast theory of Chebyshev and residual polynomials and their asymptotic behavior. The former ones maximize the leading coefficient and the latter ones maximize the point evaluation with respect to an $L^\infty$ norm. We study Chebyshev and residual extremal problems for rational functions with real poles with respect to subsets of $\overline{\mathbb{R}}$. We prove root asymptotics under fairly general assumptions on the sequence of poles. Moreover, we prove Szeg\H{o}--Widom asymptotics for sets which are regular for the Dirichlet problem and obey the Parreau--Widom and DCT conditions.

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Benjamin Eichinger, Milivoje Lukić, Giorgio Young. 2021-01-05. Asymptotics of Chebyshev rational functions with respect to subsets of the real line. https://arxiv.org/abs/2101.01744

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