Title

Kernel approximation on manifolds II: The L∞ norm of the L2 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 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

Keywords

Least squares approximation, Manifold, Positive definite kernels, Sobolev spaces

Publication Date

5-30-2011

Journal Title

SIAM Journal on Mathematical Analysis

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