no. 12
Functional analysis
Positivity improvement and Gaussian kernels
[Positivité améliorée et noyaux gaussiens]

Présenté par : Gilles Pisier

Barthe, Franck1 ; Wolff, Paweł2, 3
1 Institut de mathématiques de Toulouse, CNRS UMR 5219, Université Paul-Sabatier, 31062 Toulouse cedex 9, France
2 Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland
3 Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-956 Warszawa, Poland
Comptes Rendus. Mathématique, Tome 352 (2014) no. 12, pp. 1017-1021.

Nous montrons qu'une propriété d'amélioration de la positivité par les opérateurs multilinéaires à noyaux gaussiens peut être déterminée, avec des constantes exactes, en testant l'opérateur uniquement sur les fonctions gaussiennes. Ce résultat peut être considéré comme une forme inverse du théorème de Lieb sur les maximiseurs des noyaux gaussiens.

We show that a positivity improving property of multilinear operators with Gaussian kernels can be determined, with sharp constants, by testing Gaussian functions only. This result can be considered as a reversed form of Lieb's theorem on maximizers of Gaussian kernels.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.09.016
Barthe, Franck 1 ; Wolff, Paweł 2, 3

1 Institut de mathématiques de Toulouse, CNRS UMR 5219, Université Paul-Sabatier, 31062 Toulouse cedex 9, France
2 Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland
3 Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-956 Warszawa, Poland 
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Barthe, Franck; Wolff, Paweł. Positivity improvement and Gaussian kernels. Comptes Rendus. Mathématique, Tome 352 (2014) no. 12, pp. 1017-1021. doi : 10.1016/j.crma.2014.09.016. http://www.numdam.org/articles/10.1016/j.crma.2014.09.016/

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