Keynote
Kernel approximation and interpolation in high order Besov spaces
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This talk presents recent progress in error estimates for approximation and interpolation by positive definite and conditionally positive definite kernels. The main theoretical focus of this talk will be on measuring kernel error in high order Besov spaces, up to the limit order determined by the kernel. For approximation problems on manifolds, we show how to employ local polynomial reproductions, recently developed for smooth algebraic varieties. We will demonstrate how this novel approach to error describes spectral localization for kernel-based pseudospectral methods on spheres.
