Generalised sk-spline interpolation on compact Abelian groups

Abstract The notion of sk-spline is generalised to arbitrary compact Abelian groups. A class of conditionally positive definite kernels on the group is identified, and a subclass corresponding to the generalised sk-spline is used for constructing interpolants, on scattered data, to continuous functions on the group. The special case of d -dimensional torus is considered and convergence rates are proved when the kernel is a product of one-dimensional kernels, and the data are gridded.

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