The aim of this paper is to investigate the cone of non-negative, radial,\udpositive-definite functions in the set of continuous functions on Rd . Elements of this\udcone admit a Choquet integral representation in terms of the extremals. The main feature\udof this article is to characterize some large classes of such extremals. In particular,\udwe show that there are many other extremals than the Gaussians, thus disproving a\udconjecture of G. Choquet, and that no reasonable conjecture can be made on the full\udset of extremals.
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