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Issue ESAIM: Proc.
Volume 20, 2007
RFMAO 05 - Rencontres Franco-Marocaines en Approximation et Optimisation 2005
Page(s) 44 - 52
DOI http://dx.doi.org/10.1051/proc:072004
Published online 13 October 2007

ESAIM: Proc., 2007, Vol. 20, pp. 44-52
DOI: 10.1051/proc:072004

Introduction aux produits tensoriels de fonctionnelles convexes

Marc ATTEIA

1, Rue Clément Ader. 31520 Ramonville-Saint-Agne France

marc.atteia@wanadoo.fr

(Published online: 13 October 2007)

Abstract
This paper gives new results on tensor products of convex functionals. It extends the work of Alexandre Grothendieck regarding to tensor products of semi-norms contained in his thesis on tensor products of topological spaces [5] and in his paper about the metric theory of topological tensor products [6].

This paper provides basic tools for the study of biconvex functionals which play an essential role in many parts of experimental sciences.


Résumé
Cet article présente des résultats nouveaux que j'ai obtenus dans l' étude systématique des produits tensoriels de fonctionnelles convexes. Il étend l'étude des produits tensoriels de semi-normes faite par Alexandre Grothendieck dans sa thèse sur les produits tensoriels topologiques[5] et dans son article sur la théorie métrique des produits tensoriels topologiques [6]. Cet article fait référence à des travaux de recherche que j'ai dirigés dans le cadre du Laboratoire d'Analyse Numérique de l'Université Paul Sabatier ([2-4]). Il pose les bases d'une théorie des fonctionnelles biconvexes qui jouent un rôle fondamental dans diffé rentes branches des sciences expérimentales.


Mathematics Subject Classification. ???, ???

Key words: Produits tensoriels topologiques, Produits tensoriels de fonctionneles convexes, Analyse convexe projective, Biconvexité


© EDP Sciences, ESAIM 2007


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