Scattered data interpolation on embedded submanifolds with restricted positive definite kernels: Sobolev error estimates (Q2903059)

Interpolation with kernel functions and radial basis functions is a frequently used approach to the approximation of multivariable data. In this context, interpolation and approximation on manifolds is particularly interesting because in high dimensions, it is not rare that the multivariable data are actually from a lower dimensional manifold (embedded submanifold) within the high dimensional space. To this end, the authors study radial basis functions from the high dimensional space restricted to a manifold and derive error estimates for the approximands, and this includes the derivation of the so-called native space and the inclusion of both smooth and nonsmooth kernels.