Â© Springer International Publishing AG, part of Springer Nature 2018. All rights reserved. This article develops direct and inverse estimates for certain finite dimensional spaces arising in kernel approximation. Both the direct and inverse estimates are based on approximation spaces spanned by local Lagrange functions which are spatially highly localized. The construction of such functions is computationally efficient and generalizes the construction given in Hangelbroek et al. (Math Comput, 2017, in press) for restricted surface splines on â„d. The kernels for which the theory applies includes the Sobolev-MatÃ©rn kernels for closed, compact, connected, Câˆž Riemannian manifolds.
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