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

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.

25 pages; minor revision; new proof of Lemma 3.9; accepted for publication in SIAM J. on Math. Anal

References in corpus (2)

• Kernel Approximation on Manifolds I: Bounding the Lebesgue Constant
• Surface Spline Approximation on SO(3)

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