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arXiv · 2008.09669

Asymptotics of Chebyshev Polynomials, V. Residual Polynomials

Jacob S. Christiansen·Barry Simon·Maxim Zinchenko
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Abstract

We study residual polynomials, $R_{x_0,n}^{(\mathfrak{e})}$, $\mathfrak{e}\subset\mathbb{R}$, $x_0\in\mathbb{R}\setminus\mathfrak{e}$, which are the degree at most $n$ polynomials with $R(x_0)=1$ that minimize the $\sup$ norm on $\mathfrak{e}$. New are upper bounds on their norms (that are optimal in some cases) and Szeg\H{o}--Widom asymptotics under fairly general circumstances. We also discuss several illuminating examples and some results in the complex case.

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BibTeXRIS

Jacob S. Christiansen, Barry Simon, Maxim Zinchenko. 2020-08-21. Asymptotics of Chebyshev Polynomials, V. Residual Polynomials. https://arxiv.org/abs/2008.09669

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