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 Lp 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 ε Lp, 1 ≤ p ≤∞.
Department(s)
Mathematics
Document Type
Article
DOI
https://doi.org/10.1137/100795334
Rights Information
© Society for Industrial and Applied Mathematics
Keywords
Least squares approximation, Manifold, Positive definite kernels, Sobolev spaces
Publication Date
5-30-2011
Recommended Citation
Hangelbroek, Thomas, Francis J. Narcowich, Xingping Sun, and Joseph D. Ward. "Kernel Approximation on Manifolds II: The L_∞ Norm of the L_2 Projector." SIAM journal on mathematical analysis 43, no. 2 (2011): 662-684.
Journal Title
SIAM Journal on Mathematical Analysis
