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.
Keywords :
Type de document :
Article dans une revue
Journal of Fourier Analysis and Applications, Springer Verlag, 2009, 15, pp.561-582. 〈10.1007/s00041-008-9057-6〉
Domaine :

Littérature citée [31 références]

https://hal.archives-ouvertes.fr/hal-00202495
Contributeur : Philippe Jaming <>
Soumis le : lundi 7 janvier 2008 - 11:34:04
Dernière modification le : jeudi 3 mai 2018 - 15:32:06
Document(s) archivé(s) le : mardi 13 avril 2010 - 15:27:52

Fichiers

positive71209.pdf
Fichiers produits par l'(les) auteur(s)

Citation

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〉

Métriques

Consultations de la notice

204

Téléchargements de fichiers