Kernel Approximation on Manifolds II: The $L_{infty}$ Norm of the $L_2$ Projector Academic Article uri icon

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 ≤∞. © 2011 Society for Industrial and Applied Mathematics.

author list (cited authors)

  • Hangelbroek, T., Narcowich, F. J., Sun, X., & Ward, J. D.

citation count

  • 16

publication date

  • January 2011