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- W4286859060 abstract "Let $Ksubset mathbb R$ be a regular compact set and let $g(z)=g_{overline{mathbb C}setminus K}(z,infty)$ be the Green function for $overline{mathbb C}setminus K$ with pole at infinity. For $delta>0$, define $$ G(delta):=max{ g(z): zin mathbb C, ,operatorname{dist}(z,K)le 2delta}. $$ Let ${ x_n}_{n=0}^infty$ be a Leja sequence of points of $K$. Then the uniform norm $|T_n|=Lambda_n, n=1,2,ldots$ of the associated interpolation operator $T_n$, i.e., the $n$-th Lebesgue constant, is bounded from above by $$ min_{delta>0}2nleft[frac{operatorname{diam}( K)}{delta}e^{nG(delta)}right]^{9/8}. $$ In particular, when $K$ is a uniformly perfect subset of $mathbb R$, the Lebesgue constants grow at most polynomially in $n$. To the best of our knowledge, the result is new even when $K$ is a finite union of intervals." @default.
- W4286859060 created "2022-07-25" @default.
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- W4286859060 date "2021-11-08" @default.
- W4286859060 modified "2023-09-25" @default.
- W4286859060 title "A simple upper bound for Lebesgue constants associated with Leja points on the real line" @default.
- W4286859060 doi "https://doi.org/10.48550/arxiv.2111.04607" @default.
- W4286859060 hasPublicationYear "2021" @default.
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