On the extremal rays of the cone of positive, positive definite functions - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Fourier Analysis and Applications Année : 2009

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

Maté Matolcsi
  • Fonction : Auteur
  • PersonId : 837209
Szilard Révesz
  • Fonction : Auteur
  • PersonId : 845769

Résumé

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.
Fichier principal
Vignette du fichier
positive71209.pdf (288.66 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00202495 , version 1 (07-01-2008)

Identifiants

Citer

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

Altmetric

Partager

Gmail Facebook X LinkedIn More