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arXiv · 1005.2424

Kernel Approximation on Manifolds II: The $L_{\infty}$-norm of the $L_2$-projector

Thomas Hangelbroek·Fran J Narcowich·Xingping Sun·Joe D Ward
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Abstract

This article addresses two topics of significant mathematical and practical interest in the theory of kernel approximation: the existence of local and stable bases and the L_p--boundedness of the least squares operator. The latter is an analogue of the classical problem in univariate spline theory, known there as the "de Boor conjecture". A corollary of this work is that for appropriate kernels the least squares projector provides universal near-best approximations for functions f\in L_p, 1\le p\le \infty.

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Thomas Hangelbroek, Fran J Narcowich, Xingping Sun, Joe D Ward. 2010-05-13. Kernel Approximation on Manifolds II: The $L_{\infty}$-norm of the $L_2$-projector. https://doi.org/10.1137/100795334

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