On the extremal rays of the cone of positive, positive definite functions

Révész, Szilárd and Jaming, Philippe and Matolcsi, Máté (2009) On the extremal rays of the cone of positive, positive definite functions. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 15 (4). pp. 561-582. ISSN 1069-5869

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Abstract

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

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