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Article overview
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Extremal polynomials on the $n$-grid | Arno B.J. Kuijlaars
; | Date: |
4 Jan 2023 | Abstract: | The $n$-grid $E_n$ consists of $n$ equally spaced points in $[-1,1]$
including the endpoints $pm 1$. The extremal polynomial $p_n^*$ is the
polynomial that maximizes the uniform norm $| p |_{[-1,1]}$ among polynomials
$p$ of degree $leq alpha n$ that are bounded by one on $E_n$. For every
$alpha in (0,1)$, we determine the limit of $frac{1}{n} log |
p_n^*|_{[-1,1]}$ as $n o infty$. The interest in this limit comes from a
connection with an impossibility theorem on stable approximation on the
$n$-grid. | Source: | arXiv, 2301.01591 | Services: | Forum | Review | PDF | Favorites |
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