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arXiv · 2108.07416

On non-local approximation properties of the binomial power functions $(1+x^q)^r$

Brock Erwin·Jeff Ledford·Kira Pierce
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Abstract

This note mainly concerns the binomial power function, defined as $(1+x^q)^{r}$. We construct systems of polynomials related to non-local approximation, which allows us to establish the density results on $C[a,b]$, where $a,b\in\mathbb{R}$. As a corollary, we show that scattered translated of power functions and certain related functions are dense in the function spaces $L^p([a,b])$, for $1\leq p <\infty$.

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Brock Erwin, Jeff Ledford, Kira Pierce. 2021-08-17. On non-local approximation properties of the binomial power functions $(1+x^q)^r$. https://arxiv.org/abs/2108.07416

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