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Positive-definite functions are very important in both the theory and applications of approximation theory, probability and statistics. In particular, identifying strictly positive-definite kernels is of great interest as interpolation problems based upon such kernels are guaranteed to have a unique solution whenever the nodes {xj} are distinct. A Bochner-type result of Schoenberg characterizes co...

A Polya criterion for (strict) positive-definiteness on the sphere