Skip to Main content Skip to Navigation
Journal articles

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

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 $\R^d$. 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 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. The last feature of this article is to show that many characterizations of positive definite functions available in the literature are actually particular cases of the Choquet integral representations we obtain.
Complete list of metadatas

Cited literature [31 references]  Display  Hide  Download
Contributor : Philippe Jaming <>
Submitted on : Monday, January 7, 2008 - 11:34:04 AM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
Document(s) archivé(s) le : Tuesday, April 13, 2010 - 3:27:52 PM


Files produced by the author(s)




Philippe Jaming, Maté Matolcsi, Szilard Révesz. On the extremal rays of the cone of positive, positive definite functions. Journal of Fourier Analysis and Applications, Springer Verlag, 2009, 15, pp.561-582. ⟨10.1007/s00041-008-9057-6⟩. ⟨hal-00202495⟩



Record views


Files downloads